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

base/message_loop/message_loop.cc

Index: base/message_loop/message_loop.cc
diff --git a/base/message_loop/message_loop.cc b/base/message_loop/message_loop.cc
index 4222c774dd58b20354d6b0e4c948efcbbf5abf1b..b3c895cb58f44f148359b9488664e6c422d81f76 100644
--- a/base/message_loop/message_loop.cc
+++ b/base/message_loop/message_loop.cc
@@ -640,6 +640,10 @@ bool MessageLoop::DoIdleWork() {
   return false;
 }
 
+TimeTicks MessageLoop::GetNewlyAddedTaskDelay() {
+  return incoming_task_queue_->GetNewlyAddedTaskDelay();
+}
+
 void MessageLoop::DeleteSoonInternal(const tracked_objects::Location& from_here,
                                      void(*deleter)(const void*),
                                      const void* object) {