When you are signed into the latest Chrome beta for Android, you won't need to sign in again on other Google websites, such as Gmail, Maps, Calendar or the search page. This is the default Desktop operation.
On the Chrome blog:
When you add more than one Google Account to your device, you'll also be automatically signed in to those accounts on the web. In addition to having your accounts a click away, your bookmarks, passwords, and other Chrome stuff will be kept in sync across your devices, using the account you choose.
It requires Requires Android 4.0 and up, and you can read more details on Google Play.
Note that elements of the forthcoming Material Design are apparently sported by the new version of the app.