Chris Brown Hustles to Courthouse -- So Fresh and So Clean Clean

Chris Brown's putting his best foot forward for his big court date today -- carrying a freshly dry-cleaned suit on one arm while leaving his L.A. home moments ago ... Rihanna close behind.

Rihanna spent the night at CB's place -- you know, helping him relax a little before he faces the judge in an hour.

As we first reported, Chris is gonna have a lot of 'splaining to do today after prosecutors accused him of lying about his community service hours.