Relanding this with fixes for the unit test failures which required addition of some more plumbing …

ui/views/controls/webview/webview.gyp

 # 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.
 
 {
   'variables': {
     'chromium_code': 1,
   },
   'targets': [
     {
       # GN version: //ui/views/controls/webview
       'target_name': 'webview',
       'type': '<(component)',
       'dependencies': [
+        '../../../aura/aura.gyp:aura',
         '../../../../base/base.gyp:base',
         '../../../../base/base.gyp:base_i18n',
         '../../../../base/third_party/dynamic_annotations/dynamic_annotations.gyp:dynamic_annotations',
         '../../../../content/content.gyp:content_browser',
         '../../../../skia/skia.gyp:skia',
         '../../../../url/url.gyp:url_lib',
         '../../../base/ui_base.gyp:ui_base',
         '../../../events/events.gyp:events',
         '../../../gfx/gfx.gyp:gfx',
         '../../../gfx/gfx.gyp:gfx_geometry',
@@ skipping 11 matching lines @@
         'unhandled_keyboard_event_handler_win.cc',
         'web_dialog_view.cc',
         'web_dialog_view.h',
         'webview.cc',
         'webview.h',
         'webview_export.h',
       ],
     },
   ],
 }