diff --git a/tensorflow_probability/python/distributions/gaussian_process_regression_model.py b/tensorflow_probability/python/distributions/gaussian_process_regression_model.py
index 9fff7be726..7b034a0f71 100644
--- a/tensorflow_probability/python/distributions/gaussian_process_regression_model.py
+++ b/tensorflow_probability/python/distributions/gaussian_process_regression_model.py
@@ -25,6 +25,7 @@
 from tensorflow_probability.python.internal import dtype_util
 from tensorflow_probability.python.internal import nest_util
 from tensorflow_probability.python.internal import parameter_properties
+from tensorflow_probability.python.internal import slicing
 from tensorflow_probability.python.internal import tensor_util
 from tensorflow_probability.python.math.psd_kernels import schur_complement
 from tensorflow.python.util import deprecation  # pylint: disable=g-direct-tensorflow-import
@@ -819,6 +820,7 @@ def _event_ndims_fn(self):
             shape_fn=parameter_properties.SHAPE_FN_NOT_IMPLEMENTED,
         ),
         kernel=parameter_properties.BatchedComponentProperties(),
+        _conditional_kernel=parameter_properties.BatchedComponentProperties(),
         observation_noise_variance=parameter_properties.ParameterProperties(
             event_ndims=0,
             shape_fn=lambda sample_shape: sample_shape[:-1],
@@ -829,3 +831,8 @@ def _event_ndims_fn(self):
             shape_fn=lambda sample_shape: sample_shape[:-1],
             default_constraining_bijector_fn=(
                 lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype)))))
+
+  def __getitem__(self, slices) -> 'GaussianProcessRegressionModel':
+    # _conditional_mean_fn is a closure over possibly-sliced values, but will
+    # be rebuilt by the constructor.
+    return slicing.batch_slice(self, dict(_conditional_mean_fn=None), slices)
diff --git a/tensorflow_probability/python/distributions/gaussian_process_regression_model_test.py b/tensorflow_probability/python/distributions/gaussian_process_regression_model_test.py
index 8d9f1ca623..71daa27df6 100644
--- a/tensorflow_probability/python/distributions/gaussian_process_regression_model_test.py
+++ b/tensorflow_probability/python/distributions/gaussian_process_regression_model_test.py
@@ -689,6 +689,25 @@ def testPrivateArgPreventsCholeskyRecomputation(self):
     self.assertAllClose(d.log_prob(y_obs), d2.log_prob(y_obs))
     self.assertEqual(mock_cholesky_fn.call_count, 2)
 
+  def test_batch_slice_precomputed_gprm(self):
+    base_kernel = exponentiated_quadratic.ExponentiatedQuadratic(
+        length_scale=tf.linspace(tf.ones([]), 2., 64), feature_ndims=0)
+    x = tf.linspace(tf.zeros([]), 1., 126)
+    y = tf.linspace(tf.zeros([]), 1.5, 162)
+    d = gprm.GaussianProcessRegressionModel.precompute_regression_model(
+        base_kernel,
+        index_points=y,
+        observation_index_points=x,
+        observations=tf.math.sin(x),
+        observation_noise_variance=1e-3)
+    self.assertEqual((64,), d.batch_shape)
+    self.assertEqual((162,), d.event_shape)
+    self.assertEqual((64, 162,), d.sample(seed=test_util.test_seed()).shape)
+
+    self.assertEqual((), d[2].batch_shape)
+    self.assertEqual((162,), d[2].event_shape)
+    self.assertEqual((162,), d[2].sample(seed=test_util.test_seed()).shape)
+
 
 class GaussianProcessRegressionModelStaticTest(
     _GaussianProcessRegressionModelTest):