Remove use of deprecated MessageLoop methods in chrome/.

chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc

Index: chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc
diff --git a/chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc b/chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc
index 49facb4127173cf513b31da2e5c967876640d9d4..a30808f405241d3de219b4d607f97e0508835b06 100644
--- a/chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc
+++ b/chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.cc
@@ -3,8 +3,11 @@
 // found in the LICENSE file.
 
 #include "base/bind.h"
+#include "base/location.h"
 #include "base/macros.h"
 #include "base/message_loop/message_loop.h"
+#include "base/single_thread_task_runner.h"
+#include "base/threading/thread_task_runner_handle.h"
 #include "chrome/browser/chrome_notification_types.h"
 #include "chrome/browser/chromeos/login/easy_unlock/easy_unlock_reauth.h"
 #include "chrome/browser/chromeos/login/lock/screen_locker.h"
@@ -94,8 +97,8 @@ class ReauthHandler : public content::NotificationObserver,
   void OnAuthSuccess(const chromeos::UserContext& user_context) override {
     callback_.Run(user_context);
     // Schedule deletion.
-    base::MessageLoopForUI::current()->PostTask(FROM_HERE,
-                                                base::Bind(&EndReauthAttempt));
+    base::ThreadTaskRunnerHandle::Get()->PostTask(
+        FROM_HERE, base::Bind(&EndReauthAttempt));
   }
 
   void OnAuthFailure(const chromeos::AuthFailure& error) override {}