Try 2 - Change how ui::Clipboard is accessed so there's only one per thread.

ui/base/clipboard/clipboard.h

 // 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.
 
 #ifndef UI_BASE_CLIPBOARD_CLIPBOARD_H_
 #define UI_BASE_CLIPBOARD_CLIPBOARD_H_
 
 #include <map>
 #include <string>
 #include <vector>
 
 #include "base/compiler_specific.h"
 #include "base/gtest_prod_util.h"
 #include "base/process.h"
 #include "base/shared_memory.h"
 #include "base/string16.h"
 #include "base/threading/thread_checker.h"
+#include "base/threading/platform_thread.h"
 #include "ui/base/ui_export.h"
 
 #if defined(TOOLKIT_GTK)
 #include <gdk/gdk.h>
 #endif
 
 #if defined(OS_ANDROID)
 #include <jni.h>
 
 #include "base/android/jni_android.h"
@@ skipping 11 matching lines @@
 typedef struct _GtkClipboard GtkClipboard;
 #endif
 
 #ifdef __OBJC__
 @class NSString;
 #else
 class NSString;
 #endif
 
 namespace ui {
+class ClipboardTest;
 
 class UI_EXPORT Clipboard : NON_EXPORTED_BASE(public base::ThreadChecker) {
  public:
   // MIME type constants.
   static const char kMimeTypeText[];
   static const char kMimeTypeURIList[];
   static const char kMimeTypeDownloadURL[];
   static const char kMimeTypeHTML[];
   static const char kMimeTypeRTF[];
   static const char kMimeTypePNG[];
@@ skipping 116 matching lines @@
         return true;
 #endif
     }
     return false;
   }
 
   static Buffer FromInt(int32 buffer) {
     return static_cast<Buffer>(buffer);
   }
 
-  Clipboard();
-  ~Clipboard();
+  // Sets the list of threads that are allowed to access the clipboard.
+  static void SetAllowedThreads(
+      const std::vector<base::PlatformThreadId>& allowed_threads);
+
+  // Returns the clipboard object for the current thread.
+  //
+  // Most implementations will have at most one clipboard which will live on
+  // the main UI thread, but Windows has tricky semantics where there have to
+  // be two clipboards: one that lives on the UI thread and one that lives on
+  // the IO thread.
+  static Clipboard* GetForCurrentThread();
+
+  // Destroys the clipboard for the current thread. Usually, this will clean up
+  // all clipboards, except on Windows. (Previous code leaks the IO thread
+  // clipboard, so it shouldn't be a problem.)
+  static void DestroyClipboardForCurrentThread();
 
   // Write a bunch of objects to the system clipboard. Copies are made of the
   // contents of |objects|. On Windows they are copied to the system clipboard.
   // On linux they are copied into a structure owned by the Clipboard object and
   // kept until the system clipboard is set again.
   void WriteObjects(Buffer buffer, const ObjectMap& objects);
 
   // On Linux/BSD, we need to know when the clipboard is set to a URL.  Most
   // platforms don't care.
 #if defined(OS_WIN) || defined(OS_MACOSX) || defined(USE_AURA) \
@@ skipping 80 matching lines @@
   // Firefox text/html
   static const FormatType& GetTextHtmlFormatType();
   static const FormatType& GetCFHDropFormatType();
   static const FormatType& GetFileDescriptorFormatType();
   static const FormatType& GetFileContentFormatZeroType();
 #endif
 
  private:
   FRIEND_TEST_ALL_PREFIXES(ClipboardTest, SharedBitmapTest);
   FRIEND_TEST_ALL_PREFIXES(ClipboardTest, EmptyHTMLTest);
+  friend class ClipboardTest;
+
+  Clipboard();
+  ~Clipboard();
 
   void DispatchObject(ObjectType type, const ObjectMapParams& params);
 
   void WriteText(const char* text_data, size_t text_len);
 
   void WriteHTML(const char* markup_data,
                  size_t markup_len,
                  const char* url_data,
                  size_t url_len);
 
@@ skipping 59 matching lines @@
   GtkClipboard* clipboard_;
   GtkClipboard* primary_selection_;
 #endif
 
   DISALLOW_COPY_AND_ASSIGN(Clipboard);
 };
 
 }  // namespace ui
 
 #endif  // UI_BASE_CLIPBOARD_CLIPBOARD_H_