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

chrome/browser/ui/views/omnibox/omnibox_view_win.cc

 // 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.
 
 #include "chrome/browser/ui/views/omnibox/omnibox_view_win.h"
 
 #include <algorithm>
 #include <locale>
 #include <string>
 
 #include <richedit.h>
 #include <textserv.h>
 
 #include "base/auto_reset.h"
 #include "base/basictypes.h"
 #include "base/i18n/rtl.h"
 #include "base/lazy_instance.h"
 #include "base/memory/ref_counted.h"
 #include "base/string_util.h"
 #include "base/utf_string_conversions.h"
 #include "base/win/iat_patch_function.h"
 #include "base/win/metro.h"
 #include "base/win/scoped_hdc.h"
 #include "base/win/scoped_select_object.h"
 #include "base/win/windows_version.h"
 #include "chrome/app/chrome_command_ids.h"
 #include "chrome/browser/autocomplete/autocomplete_input.h"
 #include "chrome/browser/autocomplete/autocomplete_match.h"
 #include "chrome/browser/autocomplete/keyword_provider.h"
-#include "chrome/browser/browser_process.h"
 #include "chrome/browser/command_updater.h"
 #include "chrome/browser/net/url_fixer_upper.h"
 #include "chrome/browser/profiles/profile.h"
 #include "chrome/browser/ui/browser.h"
 #include "chrome/browser/ui/omnibox/omnibox_edit_controller.h"
 #include "chrome/browser/ui/omnibox/omnibox_popup_model.h"
 #include "chrome/browser/ui/views/location_bar/location_bar_view.h"
 #include "chrome/browser/ui/views/omnibox/omnibox_view_views.h"
 #include "chrome/common/chrome_notification_types.h"
 #include "content/public/browser/user_metrics.h"
@@ skipping 1285 matching lines @@
   if (text.empty())
     return;
 
   CHARRANGE sel;
   GURL url;
   bool write_url = false;
   GetSel(sel);
   // GetSel() doesn't preserve selection direction, so sel.cpMin will always be
   // the smaller value.
   model()->AdjustTextForCopy(sel.cpMin, IsSelectAll(), &text, &url, &write_url);
-  ui::ScopedClipboardWriter scw(g_browser_process->clipboard(),
+  ui::ScopedClipboardWriter scw(ui::Clipboard::GetForCurrentThread(),
                                 ui::Clipboard::BUFFER_STANDARD);
   scw.WriteText(text);
   if (write_url)
     scw.WriteBookmark(text, url.spec());
 }
 
 LRESULT OmniboxViewWin::OnCreate(const CREATESTRUCTW* /*create_struct*/) {
   if (base::win::IsTsfAwareRequired()) {
     // Enable TSF support of RichEdit.
     SetEditStyle(SES_USECTF, SES_USECTF);
@@ skipping 1294 matching lines @@
   return (rect.left - client_rect.left) + (client_rect.right - rect.right);
 }
 
 int OmniboxViewWin::WidthNeededToDisplay(const string16& text) const {
   // Use font_.GetStringWidth() instead of
   // PosFromChar(location_entry_->GetTextLength()) because PosFromChar() is
   // apparently buggy. In both LTR UI and RTL UI with left-to-right layout,
   // PosFromChar(i) might return 0 when i is greater than 1.
   return font_.GetStringWidth(text) + GetHorizontalMargin();
 }