Remove remaining calls to deprecated MessageLoop methods on Mac.

chrome/browser/ui/cocoa/one_click_signin_dialog_controller.mm

 // Copyright (c) 2013 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.
 
 #import "chrome/browser/ui/cocoa/one_click_signin_dialog_controller.h"
 
 #include "base/bind.h"
-#include "base/message_loop/message_loop.h"
+#include "base/threading/thread_task_runner_handle.h"
 #import "chrome/browser/ui/cocoa/constrained_window/constrained_window_custom_sheet.h"
 #include "chrome/browser/ui/cocoa/constrained_window/constrained_window_custom_window.h"
 #import "chrome/browser/ui/cocoa/one_click_signin_view_controller.h"
 
 OneClickSigninDialogController::OneClickSigninDialogController(
     content::WebContents* web_contents,
     const BrowserWindow::StartSyncCallback& sync_callback,
     const base::string16& email) {
   base::Closure close_callback = base::Bind(
       &OneClickSigninDialogController::PerformClose, base::Unretained(this));
@@ skipping 14 matching lines @@
   constrained_window_ =
       CreateAndShowWebModalDialogMac(this, web_contents, sheet);
 }
 
 OneClickSigninDialogController::~OneClickSigninDialogController() {
 }
 
 void OneClickSigninDialogController::OnConstrainedWindowClosed(
   ConstrainedWindowMac* window) {
   [view_controller_ viewWillClose];
-  base::MessageLoop::current()->DeleteSoon(FROM_HERE, this);
+  base::ThreadTaskRunnerHandle::Get()->DeleteSoon(FROM_HERE, this);
 }
 
 void OneClickSigninDialogController::PerformClose() {
   constrained_window_->CloseWebContentsModalDialog();
 }