Floyd Mayweather -- Ballin' Out with Chris Brown ... at MJ's Private Gym

It was Chris Brown dishin' off to Floyd Mayweather ... at one of the most exclusive private basketball games in the country last night -- when the stars hit up Michael Jordan's legendary court in NYC.

It all went down at Terminal 23 in New York ... a state-of-the-art hoops facility designed by Jordan Brand.

We're told there was an ultra-private game last night ... and the guest list was pretty tight -- with NBA stars like JaVale McGee and Mason Plumlee ballin' out with stars like Floyd, Chris and rapper Juelz Santana.

As for Floyd, our sources say he looked pretty good out there ... hitting a few impressive jump shots along the way.