I've not tried it yet, but supposedly unity-webapps-gmail can do what you need. If it works right, Firefox or Chromium might actually suggest you install it instead of you having to figure it out manually.
If you have a Google Apps for Your Domain account, you'll need to wait a bit longer until that works too.
The problem is gmail has to be open in your browser for the web app to do anything. It needs to work all the time.