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

base/message_loop/incoming_task_queue.cc

Index: base/message_loop/incoming_task_queue.cc
diff --git a/base/message_loop/incoming_task_queue.cc b/base/message_loop/incoming_task_queue.cc
index 5e9a4613da1cad2a28369aa78b69e87001ad9e9f..642222efc8f0e541a8876bb45c037a67c466941d 100644
--- a/base/message_loop/incoming_task_queue.cc
+++ b/base/message_loop/incoming_task_queue.cc
@@ -119,6 +119,11 @@ void IncomingTaskQueue::StartScheduling() {
     ScheduleWork();
 }
 
+TimeTicks IncomingTaskQueue::GetNewlyAddedTaskDelay() {
+  return !incoming_queue_.empty() ? incoming_queue_.front().delayed_run_time :
+      TimeTicks();
+}
+
 IncomingTaskQueue::~IncomingTaskQueue() {
   // Verify that WillDestroyCurrentMessageLoop() has been called.
   DCHECK(!message_loop_);