Add base::RunLoop and update ui_test_utils to use it to reduce flakiness

ash/accelerators/nested_dispatcher_controller.cc

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "ash/accelerators/nested_dispatcher_controller.h"
 
 #include "ash/accelerators/accelerator_dispatcher.h"
 #include "ash/shell.h"
+#include "base/run_loop.h"
 
 namespace ash {
 
 NestedDispatcherController::NestedDispatcherController() {
 }
 
 NestedDispatcherController::~NestedDispatcherController() {
 }
 
 void NestedDispatcherController::RunWithDispatcher(
     MessageLoop::Dispatcher* nested_dispatcher,
     aura::Window* associated_window,
     bool nestable_tasks_allowed) {
   MessageLoopForUI* loop = MessageLoopForUI::current();
   bool did_allow_task_nesting = loop->NestableTasksAllowed();
   loop->SetNestableTasksAllowed(nestable_tasks_allowed);
 
   AcceleratorDispatcher dispatcher(nested_dispatcher, associated_window);
 
-  loop->RunWithDispatcher(&dispatcher);
+  // TODO(jbates) crbug.com/134753 Find quitters of this RunLoop and have them
+  //              use run_loop.QuitClosure().
+  base::RunLoop run_loop(&dispatcher);
+  run_loop.Run();
   loop->SetNestableTasksAllowed(did_allow_task_nesting);
 }
 
 }  // namespace ash