Use the Chrome Identity API to authenticate users: the getAuthToken for users logged into their Google Account and the launchWebAuthFlow for users logged into a non-Google account. If your app uses its own server to authenticate users, you will need to use the latter.
from https://developer.chrome.com/apps/app_identity.
Here's an example of an app that implements the Identity API: https://github.com/GoogleChrome/chrome-app-samples/blob/master/github-auth/index.js