Chrome.identity not available/undefined
It may require providing a "key" value in your manifest as well (if you're trying to get it working locally and it's not working). You can either use the same key as the one you get when you upload your extension to the webstore or try packing an extension to generate a new one (though I couldn't get this second approach working myself).
The reason I was not able to use identity was because I was trying to access it from a content script. I switched to a background script and it works now! Thanks Rob!
PS! You also need to have "permissions": ["identity"]
set in your manifest.json
.