Create a more robust web app by adding a bit of back-end development to your Chrome Extension; made easy by the folks at Google. I'll show you how to integrate the Google OAuth2 protocol into your Chrome Extension. Doing so will allow you to gain access to your user's Google data; specfically in this video, their Contacts data.
We'll first "register" our extension to get a unique key, then we'll head on over to the Google Developer's console to get ourselves an OAuth2 Client ID and an API key for Google's People API.
Finally, I'll show you the work flow involved in getting an access or authorization token from Google's OAuth2 endpoint then using that to manipulate a users Contacts list.