Notification badges are only supported on Android.

chrome/browser/notifications/platform_notification_service_impl.cc

 // Copyright 2014 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/notifications/platform_notification_service_impl.h"
 
 #include <utility>
 #include <vector>
 
 #include "base/command_line.h"
@@ skipping 451 matching lines @@
       origin, notification_data.tag, message_center::RichNotificationData(),
       delegate);
 
   notification.set_context_message(
       DisplayNameForContextMessage(profile, origin));
   notification.set_vibration_pattern(notification_data.vibration_pattern);
   notification.set_timestamp(notification_data.timestamp);
   notification.set_renotify(notification_data.renotify);
   notification.set_silent(notification_data.silent);
 
+  // Badges are only supported on Android, primarily because it's the only
+  // platform that makes good use of them in the status bar.
+  // TODO(mvanouwerkerk): ensure no badge is loaded when it will not be used.
+#if defined(OS_ANDROID)
   // TODO(peter): Handle different screen densities instead of always using the
   // 1x bitmap - crbug.com/585815.
   notification.set_small_image(
       gfx::Image::CreateFrom1xBitmap(notification_resources.badge));
+#endif  // defined(OS_ANDROID)
 
   // Developer supplied action buttons.
   std::vector<message_center::ButtonInfo> buttons;
   for (size_t i = 0; i < notification_data.actions.size(); i++) {
     message_center::ButtonInfo button(notification_data.actions[i].title);
     // TODO(peter): Handle different screen densities instead of always using
     // the 1x bitmap - crbug.com/585815.
     button.icon =
         gfx::Image::CreateFrom1xBitmap(notification_resources.action_icons[i]);
     buttons.push_back(button);
@@ skipping 53 matching lines @@
   }
 #endif
 
   return base::string16();
 }
 
 void PlatformNotificationServiceImpl::SetNotificationDisplayServiceForTesting(
     NotificationDisplayService* display_service) {
   test_display_service_ = display_service;
 }