The below is from a BBC documentary on the Hotel Chelsea, it includes footage of Andy Warhol (inexplicably wearing headphones) sharing a meal with William S Burroughs and Nico singing "Chelsea Girls".

It was filmed inside the Chelsea Hotel in 1980, and the hotel's blog has more insight in the form of a letter from Joe Bidewell (who plays guitar in the background as Nico is singing) on what went down during filming:

"Nico's performance is spot-on, in my opinion. We rehearsed for that taping in my room # 332. The BBC filmed us in a bigger, nicer suite on another floor in the hotel.

The scene where Burroughs and Warhol are eating dinner, with the fellow reporting details to the camera at the door - nice editing, BBC. That British crew literally moved in and lived at the Chelsea for weeks, maybe longer - a month or two - just to shoot all the footage, and to get it right.

They seemed to really enjoy themselves. It was fun having them around. Some of the crew came to one of my performances at a club called s.n.a.f.u., just around the corner from the Chelsea. It was owned by Lou Tatoo, and the walls were adorned w/ Robert Mapplethorpe prints."