Chris Brown -- Doing Couples Stuff ... It's a Bitch

Chris Brown may be out of the dog house with Karrueche Tran ... but now he's stuck dragging her new pooch everywhere -- meaning he's officially back to boyfriend duties.

The on-again/off-again couple hit up Nike Town in Beverly Hills on Friday while parading the dog Chris apparently bought her for Christmas -- but did not flash any new rocks.

Remember, on Christmas Karrueche posted what looked like an engagement ring -- but that's highly unlikely since it was on the wrong hand in the Insta pic (which she's now deleted)-- AND she didn't flaunt it for cameras yesterday.

So, the only remaining question -- who picks up the poop?