Have you see it yet? You get to it in Google Play Music by click the gear icon then clicking Labs. Then enable Google Play Music for Chrome and save your changes. 
Then when you are playing some music you can pop out the mini player to control your music. Even click the dice in the middle to start listening to a random song from your library.

That is all great and everything but I have to have the full Chrome browser up and running. Granted, that is most of the time, but there are other apps that can continue running in the back ground if you have allowed them to do that. I think if I could do that with the Music app it would get more use.

If you haven't looked at any of the other Labs items, have a look at the descriptions of them and give them a try as well.