diff --git a/tensorflow_probability/python/distributions/categorical_test.py b/tensorflow_probability/python/distributions/categorical_test.py
index 6d9644cc20..b4ae3b4ec0 100644
--- a/tensorflow_probability/python/distributions/categorical_test.py
+++ b/tensorflow_probability/python/distributions/categorical_test.py
@@ -338,6 +338,19 @@ def testEntropyGradient(self):
                           res["categorical_entropy"])
       self.assertAllClose(res["true_entropy_g"],
                           res["categorical_entropy_g"])
+     
+
+  def testEntropyWithZeroProbabilities(self):
+    probs = [[0, 0.5, 0.5], [0, 1, 0]]
+    dist = categorical.Categorical(probs=probs)
+    dist_entropy = dist.entropy()
+
+    with self.cached_session():
+      self.assertAllClose(dist_entropy.eval(), 
+                          [
+                            -(0.5*np.log(0.5) + 0.5*np.log(0.5)),
+                            -(np.log(1))
+                          ])
 
   def testSample(self):
     with self.cached_session():