They're on-screen lovers in their new pic, The Words, and have been rumored to be an off-screen couple as well, but not until Friday night at the Sundance Film Festival did Bradley Cooper and Zoe Saldana let their guard down in a public place.

After doing the red carpet -- separately -- in support of the film, the two rendezvoused in the Vista Room at the Montage Deer Valley, reports Red Carpet Roxy.  Sitting on the couch in front of the fireplace, a source says, “They couldn’t keep their hands off each other!”

Zoe sipped on champagne -- of course -- while the pair engaged in some discreet canoodling.

Saldana broke up with her boyfriend of 11 years last November. Cooper has had a series of gorgeous Hollywood women on his arm, including Renée Zellweger, Cameron Diaz and Jennifer Lopez.

Bradley Cooper is a busy busy guy -- and we are not just talking about his work life!

People magazine’s Sexiest Man Alive is reportedly dating his The Words co-star, Zoe Saldana, hot on the heels of French actress Melanie Laurent and Latina lovely Jennifer Lopez.

In a case of life imitating art, after a series of on-camera hookups in June, the sexy twosome are now locking lips off-camera.