Enabled pressing TAB to cycle through the Omnibox results.

chrome/browser/ui/gtk/omnibox/omnibox_view_gtk.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/gtk/omnibox/omnibox_view_gtk.h"
 
 #include <gdk/gdkkeysyms.h>
 #include <gtk/gtk.h>
 
 #include <algorithm>
@@ skipping 537 matching lines @@
 
 void OmniboxViewGtk::SetUserText(const string16& text) {
   SetUserText(text, text, true);
 }
 
 void OmniboxViewGtk::SetUserText(const string16& text,
                                  const string16& display_text,
                                  bool update_popup) {
   model_->SetUserText(text);
   // TODO(deanm): something about selection / focus change here.
-  SetWindowTextAndCaretPos(display_text, display_text.length());
-  if (update_popup)
-    UpdatePopup();
-  TextChanged();
+  SetWindowTextAndCaretPos(display_text, display_text.length(), update_popup,
+      true);
 }
 
 void OmniboxViewGtk::SetWindowTextAndCaretPos(const string16& text,
-                                              size_t caret_pos) {
+                                              size_t caret_pos,
+                                              bool update_popup,
+                                              bool notify_text_changed) {
   CharRange range(static_cast<int>(caret_pos), static_cast<int>(caret_pos));
   SetTextAndSelectedRange(text, range);
+
+  if (update_popup)
+    UpdatePopup();
+
+  if (notify_text_changed)
+    TextChanged();
 }
 
 void OmniboxViewGtk::SetForcedQuery() {
   const string16 current_text(GetText());
   const size_t start = current_text.find_first_not_of(kWhitespaceUTF16);
   if (start == string16::npos || (current_text[start] != '?')) {
     SetUserText(ASCIIToUTF16("?"));
   } else {
     StartUpdatingHighlightedText();
     SetSelectedRange(CharRange(current_text.size(), start + 1));
@@ skipping 54 matching lines @@
   model_->StopAutocomplete();
 }
 
 void OmniboxViewGtk::OnTemporaryTextMaybeChanged(
     const string16& display_text,
     bool save_original_selection) {
   if (save_original_selection)
     saved_temporary_selection_ = GetSelection();
 
   StartUpdatingHighlightedText();
-  SetWindowTextAndCaretPos(display_text, display_text.length());
+  SetWindowTextAndCaretPos(display_text, display_text.length(), false, false);
   FinishUpdatingHighlightedText();
   TextChanged();

[aaron.randolph, 2012/01/14 04:25:34]

It looks like this could probably be removed and true passed to
SetWindowTextAndCaretPos but I can't test it to verify.

[Peter Kasting, 2012/01/18 18:41:31]

I looked at this with one of the GTK guys and neither of us are sure either. 
Since it's not a big deal let's just leave this as-is.

 }
 
 bool OmniboxViewGtk::OnInlineAutocompleteTextMaybeChanged(
     const string16& display_text,
     size_t user_text_length) {
   if (display_text == GetText())
     return false;
 
   StartUpdatingHighlightedText();
   CharRange range(display_text.size(), user_text_length);
@@ skipping 1737 matching lines @@
 
   // Make all the children of the widget visible. NOTE: this won't display
   // anything, it just toggles the visible flag.
   gtk_widget_show_all(omnibox_view->GetNativeView());
   // Hide the widget. NativeViewHostGtk will make it visible again as necessary.
   gtk_widget_hide(omnibox_view->GetNativeView());
 
   return omnibox_view;
 }
 #endif