diff --git a/tornado/ioloop.py b/tornado/ioloop.py
index dfbb462b..5f01223b 100644
--- a/tornado/ioloop.py
+++ b/tornado/ioloop.py
@@ -679,8 +679,8 @@ class PeriodicCallback(object):
     """
     def __init__(self, callback, callback_time, io_loop=None):
         self.callback = callback
-        if callback_time == 0:
-            raise ValueError("Periodic callback cannot have a period of 0ms")
+        if callback_time <= 0:
+            raise ValueError("Periodic callback must have a positive callback_time")
         self.callback_time = callback_time
         self.io_loop = io_loop or IOLoop.instance()
         self._running = False