Chris Brown & Rihanna GO PUBLIC -- Getting Physical in NYC

Chris Brown and Rihanna are barely trying to hide it anymore -- getting up close and personal at a NYC nightclub late Monday night ... then carousing at Rihanna's hotel for hours.

Chris and Rihanna hit up Griffin nightclub in the Meatpacking District -- we're told they arrived 5 minutes apart, and quickly ended up at the same table. Sources inside the club say the two were all over each other, and even disappeared together in a bathroom for 20 minutes.

People inside the club say the duo were kissing and hugging out in the open.

The two left the club separately -- but hours later, Chris was spotted leaving the Gansevoort Hotel, where Rihanna was staying.

By the way, Tuesday afternoon, Chris' clueless GF Karrueche tweeted that Chris sent her roses, a teddy bear and chocolates -- maybe a lame, "I'm sorry."

So we gotta ask ...