Replace deprecated base::NonThreadSafe in chrome in favor of SequenceChecker.

chrome/browser/process_singleton_startup_lock.h

Index: chrome/browser/process_singleton_startup_lock.h
diff --git a/chrome/browser/process_singleton_startup_lock.h b/chrome/browser/process_singleton_startup_lock.h
index 9aa69adcfbc8e5b1aa483e76eb38371067e7456d..eb3d1fcf65d6a6e5ad67e3df0de30eaa3d208adf 100644
--- a/chrome/browser/process_singleton_startup_lock.h
+++ b/chrome/browser/process_singleton_startup_lock.h
@@ -12,7 +12,7 @@
 #include "base/command_line.h"
 #include "base/files/file_path.h"
 #include "base/macros.h"
-#include "base/threading/non_thread_safe.h"
+#include "base/sequence_checker.h"
 #include "chrome/browser/process_singleton.h"
 
 // Provides a ProcessSingleton::NotificationCallback that can queue up
@@ -23,7 +23,7 @@
 // when the process is prepared to handle command-line invocations.
 //
 // Once unlocked, notifications are forwarded to a wrapped NotificationCallback.
-class ProcessSingletonStartupLock : public base::NonThreadSafe {
+class ProcessSingletonStartupLock {
  public:
   explicit ProcessSingletonStartupLock(
       const ProcessSingleton::NotificationCallback& original_callback);
@@ -51,6 +51,8 @@ class ProcessSingletonStartupLock : public base::NonThreadSafe {
   std::vector<DelayedStartupMessage> saved_startup_messages_;
   ProcessSingleton::NotificationCallback original_callback_;
 
+  SEQUENCE_CHECKER(sequence_checker_);
+
   DISALLOW_COPY_AND_ASSIGN(ProcessSingletonStartupLock);
 };