diff --git a/docs/jax.random.rst b/docs/jax.random.rst
index 1d7f68e39..64873b727 100644
--- a/docs/jax.random.rst
+++ b/docs/jax.random.rst
@@ -30,6 +30,7 @@ List of Available Functions
     fold_in
     gamma
     generalized_normal
+    geometric
     gumbel
     laplace
     loggamma
diff --git a/jax/_src/random.py b/jax/_src/random.py
index 1f2a46a9d..aa50abdce 100644
--- a/jax/_src/random.py
+++ b/jax/_src/random.py
@@ -2098,3 +2098,53 @@ def _wald(key, mean, shape, dtype) -> Array:
   x = mean + mean_sq * y / 2 - mean / 2 * sqrt_term
   w = lax.select(lax.le(z,  mean / (mean + x)), x, mean_sq / x)
   return w
+
+def geometric(key: KeyArray,
+              p: RealArray,
+              shape: Optional[Shape] = None,
+              dtype: DTypeLikeInt = dtypes.int_) -> Array:
+  r"""Sample Geometric random values with given shape and float dtype.
+
+  The values are returned according to the probability mass function:
+
+  .. math::
+      f(k;p) = p(1-p)^{k-1}
+
+  on the domain :math:`0 < p < 1`.
+
+  Args:
+    key: a PRNG key used as the random key.
+    p: a float or array of floats broadcast-compatible with ``shape``
+      representing the the probability of success of an individual trial.
+    shape: optional, a tuple of nonnegative integers specifying the result
+      shape. Must be broadcast-compatible with ``p``. The default
+      (None) produces a result shape equal to ``np.shape(p)``.
+    dtype: optional, a int dtype for the returned values (default int64 if
+      jax_enable_x64 is true, otherwise int32).
+
+  Returns:
+    A random array with the specified dtype and with shape given by ``shape`` if
+    ``shape`` is not None, or else by ``p.shape``.
+  """
+  key, _ = _check_prng_key(key)
+  if not dtypes.issubdtype(dtype, np.integer):
+    raise ValueError("dtype argument to `geometric` must be an int "
+                     f"dtype, got {dtype}")
+  dtype = dtypes.canonicalize_dtype(dtype)
+  if shape is not None:
+    shape = core.canonicalize_shape(shape)
+  return _geometric(key, p, shape, dtype)
+
+@partial(jit, static_argnums=(2, 3), inline=True)
+def _geometric(key, p, shape, dtype) -> Array:
+  if shape is None:
+    shape =  np.shape(p)
+  else:
+    _check_shape("geometric", shape, np.shape(p))
+  check_arraylike("geometric", p)
+  p, = promote_dtypes_inexact(p)
+  u = uniform(key, shape, p.dtype)
+  log_u = lax.log(u)
+  log_one_minus_p = lax.log1p(-p)
+  g = lax.floor(lax.div(log_u, log_one_minus_p)) + 1
+  return g.astype(dtype)
diff --git a/jax/random.py b/jax/random.py
index 8a84098f7..6cbcd9739 100644
--- a/jax/random.py
+++ b/jax/random.py
@@ -163,6 +163,7 @@ from jax._src.random import (
   fold_in as fold_in,
   gamma as gamma,
   generalized_normal as generalized_normal,
+  geometric as geometric,
   gumbel as gumbel,
   key_data as key_data,
   laplace as laplace,
diff --git a/tests/random_test.py b/tests/random_test.py
index cdf46e6ad..78732c9fe 100644
--- a/tests/random_test.py
+++ b/tests/random_test.py
@@ -1551,6 +1551,22 @@ class LaxRandomTest(jtu.JaxTestCase):
     for samples in [uncompiled_samples, compiled_samples]:
       self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.invgauss(mu=mean).cdf)
 
+  @jtu.sample_product(
+      p= [0.2, 0.3, 0.4, 0.5 ,0.6],
+      dtype= [np.int16, np.int32, np.int64])
+  def testGeometric(self, p, dtype):
+    key = self.seed_prng(1)
+    rand = lambda key: random.geometric(key, p, shape=(10000, ), dtype=dtype)
+    crand = jax.jit(rand)
+
+    uncompiled_samples = rand(key)
+    compiled_samples = crand(key)
+
+    for samples in [uncompiled_samples, compiled_samples]:
+      self._CheckChiSquared(samples, scipy.stats.geom(p).pmf)
+      self.assertAllClose(samples.mean(), 1 / p, rtol=0.02, check_dtypes=False)
+      self.assertAllClose(samples.var(), (1 - p) / (p * p) , rtol=0.05, check_dtypes=False)
+
 class KeyArrayTest(jtu.JaxTestCase):
   # Key arrays involve:
   # * a Python key array type, backed by an underlying uint32 "base" array,