diff --git a/jax/_src/api.py b/jax/_src/api.py
index c01bd14ca..0a9901b96 100644
--- a/jax/_src/api.py
+++ b/jax/_src/api.py
@@ -81,6 +81,7 @@ from jax.interpreters.invertible_ad import custom_ivjp
 from jax.custom_batching import custom_vmap
 from jax.custom_derivatives import (closure_convert, custom_gradient, custom_jvp,
                                     custom_vjp, linear_call)
+from jax.custom_transpose import custom_transpose
 from jax.ad_checkpoint import checkpoint_policies
 
 from jax._src.config import (flags, config, bool_env,
diff --git a/jax/_src/custom_transpose.py b/jax/_src/custom_transpose.py
new file mode 100644
index 000000000..316cfde83
--- /dev/null
+++ b/jax/_src/custom_transpose.py
@@ -0,0 +1,134 @@
+# Copyright 2022 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import functools
+from typing import Callable, Optional
+
+from jax import core
+from jax import linear_util as lu
+from jax.interpreters import ad
+from jax.interpreters import partial_eval as pe
+from jax.interpreters import mlir
+from jax.interpreters import xla
+from jax.tree_util import (tree_flatten, tree_leaves, tree_unflatten,
+                           treedef_tuple)
+from jax._src import ad_util
+from jax._src import source_info_util
+from jax._src import traceback_util
+from jax._src import util
+from jax._src.api_util import flatten_fun_nokwargs
+
+
+source_info_util.register_exclusion(__file__)
+traceback_util.register_exclusion(__file__)
+
+
+map, unsafe_map = util.safe_map, map
+zip, unsafe_zip = util.safe_zip, zip
+
+
+class custom_transpose:
+  fun: Callable
+  transpose: Optional[Callable]
+
+  def __init__(self, fun: Callable):
+    self.fun = fun  # type: ignore[assignment]
+    self.transpose = None
+    functools.update_wrapper(self, fun)
+
+  def def_transpose(self, transpose: Callable):
+    self.transpose = transpose
+    return transpose
+
+  @traceback_util.api_boundary
+  def __call__(self, residual_arg, linear_arg):
+    res_arg, lin_arg = residual_arg, linear_arg
+    _, res_tree = tree_flatten(res_arg)
+    _, lin_tree = tree_flatten(lin_arg)
+    args_flat, in_tree = tree_flatten((res_arg, lin_arg))
+
+    flat_fun, out_tree = flatten_fun_nokwargs(lu.wrap_init(self.fun), in_tree)
+    in_avals = [core.raise_to_shaped(core.get_aval(x)) for x in args_flat]
+    debug = pe.debug_info(self.fun, in_tree, False, "custom_transpose")
+    jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(flat_fun, in_avals, debug)
+    assert not len(consts)
+    closed_call = core.ClosedJaxpr(pe.convert_constvars_jaxpr(jaxpr), ())
+    out_flat = custom_transpose_p.bind(*consts, *args_flat,
+                                       call=closed_call,
+                                       rule=self.transpose,
+                                       lin_tree=lin_tree,
+                                       res_tree=res_tree,
+                                       out_tree=out_tree())
+    return tree_unflatten(out_tree(), out_flat)
+
+
+### utils
+
+def rule_name(rule):
+  return getattr(rule, '__name__', '<unnamed transpose rule>')
+
+def check_transpose_rule_trees(rule, lin_tree, rule_out_tree):
+  if lin_tree != rule_out_tree and len(lin_tree.children()) == 1:
+    lin_tree2, = lin_tree.children()
+  else:
+    lin_tree2 = lin_tree
+  if lin_tree2 != rule_out_tree:
+    raise ValueError(
+        'structure of custom transpose rule\'s output does not match '
+        'structure of primal function\'s linear inputs under '
+        f'custom transpose rule ({rule_name(rule)}).\n'
+        f'Transpose rule output: {rule_out_tree}\n'
+        f'Linear primal inputs: {lin_tree}')
+
+
+### custom_transpose_p rules
+
+
+def custom_transpose_impl(*args, call, rule, res_tree, lin_tree, out_tree):
+  del rule, res_tree, lin_tree, out_tree
+  return core.jaxpr_as_fun(call)(*args)
+
+
+def custom_transpose_transpose_rule(
+    cts, *args, call, rule, res_tree, lin_tree, out_tree):
+  call_in_tree = treedef_tuple((res_tree, lin_tree))
+
+  res_arg, lin_arg = tree_unflatten(call_in_tree, args)
+  assert all(ad.is_undefined_primal(x)     for x in tree_leaves(lin_arg))
+  assert all(not ad.is_undefined_primal(x) for x in tree_leaves(res_arg))
+
+  cts = [ad_util.zeros_like_aval(ct_aval) if type(ct) is ad_util.Zero else ct
+         for ct, ct_aval in zip(cts, call.out_avals)]
+  ct_out = tree_unflatten(out_tree, cts)
+  ct_lin = rule(res_arg, ct_out)
+  ct_lin_flat, ct_lin_tree = tree_flatten(ct_lin)
+  check_transpose_rule_trees(rule, lin_tree, ct_lin_tree)
+  return [None] * len(tree_leaves(res_arg)) + ct_lin_flat
+
+
+def custom_transpose_abstract_eval(*in_avals, call, **_):
+  return call.out_avals
+
+
+custom_transpose_p = core.Primitive('custom_transpose_call')
+custom_transpose_p.multiple_results = True
+custom_transpose_p.def_impl(custom_transpose_impl)
+custom_transpose_p.def_abstract_eval(custom_transpose_abstract_eval)
+ad.primitive_transposes[custom_transpose_p] = custom_transpose_transpose_rule
+xla.register_translation(custom_transpose_p,
+                         xla.lower_fun(custom_transpose_impl, new_style=True,
+                                       multiple_results=True),
+                         initial_style=True)
+mlir.register_lowering(custom_transpose_p, mlir.lower_fun(
+    custom_transpose_impl, multiple_results=True))
diff --git a/jax/custom_transpose.py b/jax/custom_transpose.py
new file mode 100644
index 000000000..1e00577c1
--- /dev/null
+++ b/jax/custom_transpose.py
@@ -0,0 +1,18 @@
+# Copyright 2022 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# flake8: noqa: F401
+from jax._src.custom_transpose import (
+  custom_transpose,
+)
diff --git a/jax/experimental/jax2tf/jax2tf.py b/jax/experimental/jax2tf/jax2tf.py
index f7956cc9e..c8ecde3f6 100644
--- a/jax/experimental/jax2tf/jax2tf.py
+++ b/jax/experimental/jax2tf/jax2tf.py
@@ -981,6 +981,7 @@ tf_not_yet_impl = [
     "after_all",
     "all_to_all",
     "create_token",
+    "custom_transpose_call",
     "infeed",
     "linear_call",
     "outfeed",
diff --git a/tests/api_test.py b/tests/api_test.py
index 042c9e2f1..d0c5613d3 100644
--- a/tests/api_test.py
+++ b/tests/api_test.py
@@ -6200,13 +6200,14 @@ class CustomVJPTest(jtu.JaxTestCase):
                     modes=['rev'])
 
 
-class CustomTransposeTest(jtu.JaxTestCase):
+def transpose_unary(f, x_example):
+  def transposed(y):
+    x, = api.linear_transpose(f, x_example)(y)
+    return x
+  return transposed
 
-  def transpose(self, f, x_example):
-    def transposed(y):
-      x, = api.linear_transpose(f, x_example)(y)
-      return x
-    return transposed
+
+class CustomTransposeTest(jtu.JaxTestCase):
 
   def test_linear_call(self):
     def f(x, y):
@@ -6223,8 +6224,8 @@ class CustomTransposeTest(jtu.JaxTestCase):
 
     f1     = lambda x: f(x, y)
     f1_ref = lambda x: f_ref(x, y)
-    self.assertAllClose(self.transpose(f1,     x)(x),
-                        self.transpose(f1_ref, x)(x))
+    self.assertAllClose(transpose_unary(f1,     x)(x),
+                        transpose_unary(f1_ref, x)(x))
 
   def test_linear_call_incorrect_transpose(self):
     def f(x, y):
@@ -6241,8 +6242,8 @@ class CustomTransposeTest(jtu.JaxTestCase):
 
     f1     = lambda x: f(x, y)
     f1_ref = lambda x: f_ref(x, 2. * y)  # nb: double the reference divisor
-    self.assertAllClose(self.transpose(f1,     x)(x),
-                        self.transpose(f1_ref, x)(x))
+    self.assertAllClose(transpose_unary(f1,     x)(x),
+                        transpose_unary(f1_ref, x)(x))
 
   def test_linear_call_transpose_transpose_transpose(self):
     def fn(r, x): return x / r
@@ -6253,9 +6254,9 @@ class CustomTransposeTest(jtu.JaxTestCase):
     x = jnp.ones(2) * 6.
     y = jnp.ones(2) * 3.
     f = lambda x: f_(x, y)
-    ft   = self.transpose(f,   x)
-    ftt  = self.transpose(ft,  x)
-    fttt = self.transpose(ftt, x)
+    ft   = transpose_unary(f,   x)
+    ftt  = transpose_unary(ft,  x)
+    fttt = transpose_unary(ftt, x)
     self.assertAllClose(ft(x), x + tp(y, x))
     self.assertAllClose(f(x),  ftt(x))
     self.assertAllClose(ft(x), fttt(x))
@@ -6277,8 +6278,8 @@ class CustomTransposeTest(jtu.JaxTestCase):
     c, x = 2., 3.
     t = [4., 5.]
     self.assertAllClose(f(c, x), f_ref(c, x))
-    self.assertAllClose(self.transpose(partial(f,     c), x)(t),
-                        self.transpose(partial(f_ref, c), x)(t))
+    self.assertAllClose(transpose_unary(partial(f,     c), x)(t),
+                        transpose_unary(partial(f_ref, c), x)(t))
 
   def test_linear_call_nested(self):
     # identity function with an untrue transpose of 0
@@ -6296,11 +6297,11 @@ class CustomTransposeTest(jtu.JaxTestCase):
       return api.linear_call(f_, t_, (), x)
 
     x = 5.
-    id_t  = self.transpose(id_,  x)
-    id_tt = self.transpose(id_t, x)
-    ft   = self.transpose(f,    x)
-    ftt  = self.transpose(ft,   x)
-    fttt = self.transpose(ftt,  x)
+    id_t  = transpose_unary(id_,  x)
+    id_tt = transpose_unary(id_t, x)
+    ft   = transpose_unary(f,    x)
+    ftt  = transpose_unary(ft,   x)
+    fttt = transpose_unary(ftt,  x)
 
     self.assertAllClose(id_(x),   x)
     self.assertAllClose(id_t(x),  0.)
@@ -6322,8 +6323,216 @@ class CustomTransposeTest(jtu.JaxTestCase):
     self.assertAllClose(f(x, y), jax.jit(f)(x, y))
 
     f1 = lambda x: f(x, y)
-    self.assertAllClose(self.transpose(f1, x)(x),
-                        jax.jit(self.transpose(f1, x))(x))
+    self.assertAllClose(transpose_unary(f1, x)(x),
+                        jax.jit(transpose_unary(f1, x))(x))
+
+  def test_basic(self):
+    def f(x, y):
+      @api.custom_transpose
+      def fn(r, x): return x / r
+      @fn.def_transpose
+      def tp(r, t): return t / r
+
+      return x + fn(y, x)
+
+    def f_ref(x, y):
+      return x + x / y
+
+    x = jnp.ones(2) * 6.
+    y = jnp.ones(2) * 3.
+    self.assertAllClose(f(x, y), f_ref(x, y))
+
+    f1     = lambda x: f(x, y)
+    f1_ref = lambda x: f_ref(x, y)
+    self.assertAllClose(transpose_unary(f1,     x)(x),
+                        transpose_unary(f1_ref, x)(x))
+
+  def test_incorrect_transpose(self):
+    def f(x, y):
+      @api.custom_transpose
+      def fn(r, x): return x / r
+      @fn.def_transpose
+      def tp(r, t): return t / (2. * r)  # nb: not the true transpose
+
+      return x + fn(y, x)
+
+    def f_ref(x, y):
+      return x + x / y
+
+    x = jnp.ones(2) * 6.
+    y = jnp.ones(2) * 3.
+    self.assertAllClose(f(x, y), f_ref(x, y))
+
+    f1     = lambda x: f(x, y)
+    f1_ref = lambda x: f_ref(x, 2. * y)  # nb: double the reference divisor
+    self.assertAllClose(transpose_unary(f1,     x)(x),
+                        transpose_unary(f1_ref, x)(x))
+
+  def test_transpose_transpose_transpose(self):
+    @api.custom_transpose
+    def fn(r, x): return x / r
+    @api.custom_transpose
+    def tp(r, t): return t / (2. * r)  # nb: untrue transpose
+
+    fn.def_transpose(tp)
+    tp.def_transpose(fn)
+
+    def f_(x, y):
+      return x + fn(y, x)
+
+    x = jnp.ones(2) * 6.
+    y = jnp.ones(2) * 3.
+    f = lambda x: f_(x, y)
+    ft   = transpose_unary(f,   x)
+    ftt  = transpose_unary(ft,  x)
+    fttt = transpose_unary(ftt, x)
+    self.assertAllClose(ft(x), x + tp(y, x))
+    self.assertAllClose(f(x),  ftt(x))
+    self.assertAllClose(ft(x), fttt(x))
+
+  def test_scalar_to_vector(self):
+    def f(c, x):
+      @api.custom_transpose
+      def fn(_, x):
+        return [x, x]
+
+      @fn.def_transpose
+      def tp(_, t):
+        t1, t2 = t
+        return t1 + t2
+
+      return fn((), c * x)
+
+    def f_ref(c, x):
+      return [c * x, c * x]
+
+    c, x = 2., 3.
+    t = [4., 5.]
+    self.assertAllClose(f(c, x), f_ref(c, x))
+    self.assertAllClose(transpose_unary(partial(f,     c), x)(t),
+                        transpose_unary(partial(f_ref, c), x)(t))
+
+  def test_nested(self):
+    # identity function with an untrue transpose of 0
+    def id_(x):
+      f = api.custom_transpose(lambda _, x: x)
+      t = api.custom_transpose(lambda _, t: 0.)
+      f.def_transpose(t)
+      t.def_transpose(f)
+      return f((), x)
+
+    # identity function with an untrue transpose of 7, and where both
+    # forward and transpose have custom transpositions that should
+    # never end up invoked.
+    def f(x):
+      f_ = api.custom_transpose(lambda _, x: id_(x))
+      t_ = api.custom_transpose(lambda _, t: id_(7.))
+      f_.def_transpose(t_)
+      t_.def_transpose(f_)
+      return f_((), x)
+
+    x = 5.
+    id_t  = transpose_unary(id_,  x)
+    id_tt = transpose_unary(id_t, x)
+    ft   = transpose_unary(f,    x)
+    ftt  = transpose_unary(ft,   x)
+    fttt = transpose_unary(ftt,  x)
+
+    self.assertAllClose(id_(x),   x)
+    self.assertAllClose(id_t(x),  0.)
+    self.assertAllClose(id_tt(x), x)
+
+    self.assertAllClose(f(x),    x)
+    self.assertAllClose(ft(x),   7.)
+    self.assertAllClose(ftt(x),  x)
+    self.assertAllClose(fttt(x), 7.)
+
+  def test_one_degree(self):
+    T = lambda f: transpose_unary(f, 0.)
+
+    @api.custom_transpose
+    def f(_, z): return 2. * z
+    @f.def_transpose
+    def ft(_, z): return 3. * z
+
+    f = partial(f, ())
+    self.assertAllClose(2., f(1.))
+    self.assertAllClose(3., T(f)(1.))
+    self.assertAllClose(3., T(T(f))(1.))
+    self.assertAllClose(3., T(T(T(f)))(1.))
+    self.assertAllClose(3., T(T(T(T(f))))(1.))  # ...
+
+  def test_two_degrees(self):
+    T = lambda f: transpose_unary(f, 0.)
+
+    @api.custom_transpose
+    def f(_, z): return 2. * z
+
+    @f.def_transpose
+    @api.custom_transpose
+    def ft(_, z): return 3. * z
+
+    @ft.def_transpose
+    def ftt(_, z): return 7. * z
+
+    f = partial(f, ())
+    self.assertAllClose(2., f(1.))
+    self.assertAllClose(3., T(f)(1.))
+    self.assertAllClose(7., T(T(f))(1.))
+    self.assertAllClose(7., T(T(T(f)))(1.))
+    self.assertAllClose(7., T(T(T(T(f))))(1.))  # ...
+
+  def test_symmetric(self):
+    T = lambda f: transpose_unary(f, 0.)
+
+    @api.custom_transpose
+    def f(_, z): return 2. * z
+    @api.custom_transpose
+    def g(_, z): return 3. * z
+
+    f.def_transpose(g)
+    g.def_transpose(f)
+
+    f = partial(f, ())
+    self.assertAllClose(2., f(1.))
+    self.assertAllClose(3., T(f)(1.))
+    self.assertAllClose(2., T(T(f))(1.))
+    self.assertAllClose(3., T(T(T(f)))(1.))
+    self.assertAllClose(2., T(T(T(T(f))))(1.))  # ...
+
+  def test_recursive(self):
+    T = lambda f: transpose_unary(f, 0.)
+
+    @api.custom_transpose
+    def f(c, z): return c * z
+
+    @f.def_transpose
+    def ft(c, z): return f(c + 1., z)
+
+    g = partial(f, 1.)
+    self.assertAllClose(1., g(1.))
+    self.assertAllClose(2., T(g)(1.))
+    self.assertAllClose(3., T(T(g))(1.))
+    self.assertAllClose(4., T(T(T(g)))(1.))
+    self.assertAllClose(5., T(T(T(T(g))))(1.))  # ...
+
+  def test_jit(self):
+    def f(x, y):
+      @api.custom_transpose
+      def fn(r, x): return x / r
+      @fn.def_transpose
+      def tp(r, t): return t / r
+
+      return x + fn(y, x)
+
+    x = jnp.ones(2) * 6.
+    y = jnp.ones(2) * 3.
+    self.assertAllClose(f(x, y), jax.jit(f)(x, y))
+
+    f_ = lambda x: f(x, y)
+    f_t = transpose_unary(f_, x)
+    self.assertAllClose(f_(x), jax.jit(f_)(x))
+    self.assertAllClose(f_t(x), jax.jit(f_t)(x))
 
 
 class CustomVmapTest(jtu.JaxTestCase):