Remove use of deprecated MessageLoop methods in chrome/.

chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc

Index: chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc
diff --git a/chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc b/chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc
index 5ac50bd4f1d502b5fe70ebcf6c7ac7ae4a0044f0..3da63d6c0ab3fe4a16dc228bba77077178be678a 100644
--- a/chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc
+++ b/chrome/browser/chromeos/login/screens/chrome_user_selection_screen.cc
@@ -10,8 +10,9 @@
 #include "base/bind.h"
 #include "base/location.h"
 #include "base/logging.h"
-#include "base/message_loop/message_loop.h"
+#include "base/single_thread_task_runner.h"
 #include "base/strings/utf_string_conversions.h"
+#include "base/threading/thread_task_runner_handle.h"
 #include "base/values.h"
 #include "chrome/browser/browser_process.h"
 #include "chrome/browser/browser_process_platform_part.h"
@@ -103,7 +104,7 @@ void ChromeUserSelectionScreen::CheckForPublicSessionDisplayNameChange(
   // and |this| are informed of the display name change is undefined. Post a
   // task that will update the UI after the UserManager is guaranteed to have
   // been informed of the change.
-  base::MessageLoop::current()->PostTask(
+  base::ThreadTaskRunnerHandle::Get()->PostTask(
       FROM_HERE,
       base::Bind(&ChromeUserSelectionScreen::SetPublicSessionDisplayName,
                  weak_factory_.GetWeakPtr(), account_id));