diff --git a/Lib/random.py b/Lib/random.py
index c89cbb755abac8..2460ac3d98601f 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -836,7 +836,11 @@ def binomialvariate(self, n=1, p=0.5):
             if not c:
                 return x
             while True:
-                y += _floor(_log2(random()) / c) + 1
+                try:
+                    y += _floor(_log2(random()) / c) + 1
+                except ValueError:
+                    # Handle rare case of where random() gives 0.0
+                    continue
                 if y > n:
                     return x
                 x += 1