Don't peek messages in the MessagePumpForUI class when we receive our kMsgHaveWork message.

base/message_loop/incoming_task_queue.h

Index: base/message_loop/incoming_task_queue.h
diff --git a/base/message_loop/incoming_task_queue.h b/base/message_loop/incoming_task_queue.h
index 7dd1e82312914cec00e239aa4698cada7307cb1c..544f3e907ee223d5ec00ad05974bd06a23181593 100644
--- a/base/message_loop/incoming_task_queue.h
+++ b/base/message_loop/incoming_task_queue.h
@@ -57,6 +57,9 @@ class BASE_EXPORT IncomingTaskQueue
   // scheduling work.
   void StartScheduling();
 
+  // Returns the delay for the most recently added task.
+  TimeTicks GetNewlyAddedTaskDelay();
+
  private:
   friend class RefCountedThreadSafe<IncomingTaskQueue>;
   virtual ~IncomingTaskQueue();