Make Widget::Show() creates active windows.

chrome/browser/ui/views/omnibox/omnibox_popup_contents_view.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_popup_contents_view.h"
 
 #include "chrome/browser/search/search.h"
 #include "chrome/browser/themes/theme_properties.h"
 #include "chrome/browser/ui/omnibox/omnibox_view.h"
 #include "chrome/browser/ui/views/location_bar/location_bar_view.h"
@@ skipping 208 matching lines @@
 #endif
     popup_->SetContentsView(this);
     popup_->StackAbove(omnibox_view_->GetRelativeWindowForPopup());
     if (!popup_.get()) {
       // For some IMEs GetRelativeWindowForPopup triggers the omnibox to lose
       // focus, thereby closing (and destroying) the popup.
       // TODO(sky): this won't be needed once we close the omnibox on input
       // window showing.
       return;
     }
-    popup_->Show();
+    popup_->ShowInactive();
   } else {
     // Animate the popup shrinking, but don't animate growing larger since that
     // would make the popup feel less responsive.
     start_bounds_ = GetWidget()->GetWindowBoundsInScreen();
     if (target_bounds_.height() < start_bounds_.height())
       size_animation_.Show();
     else
       start_bounds_ = target_bounds_;
     popup_->SetBounds(GetPopupBounds());
   }
@@ skipping 256 matching lines @@
   size_t index = GetIndexForPoint(event.location());
   if (!HasMatchAt(index))
     return;
   omnibox_view_->OpenMatch(model_->result().match_at(index), disposition,
                            GURL(), index);
 }
 
 OmniboxResultView* OmniboxPopupContentsView::result_view_at(size_t i) {
   return static_cast<OmniboxResultView*>(child_at(static_cast<int>(i)));
 }