Google Chrome push-notifications without browser running
There is some nuance to this:
Chrome for Android: Push messages will wake up the Service Worker and Web App even if the browser is closed. This is the default and our ideal position across all platforms
Desktop Chrome: Push works and will wake up the service worker if the browser is still open. However it will not work if the browser is closed. You can force the browser to remain open if you have a Chrome App that is set to run in the background. Other than that we (the Chrome team) are working out how we enable this by default on Windows, Mac and Linux.
Chrome for iOS: Push just does not work on this platform
Chromium blog has a post with code examples: http://updates.html5rocks.com/2015/03/push-notificatons-on-the-open-web
And the documentation was updated too: https://developer.chrome.com/apps/cloudMessaging
It is possible to write Chrome extension where background script can run if Chrome is allowed to run in the background (configurable in settings) and it can use GCM.