The West Wing star, who portrayed a presidential aide on the hit Tv drama, joined his castmates at the Waldorf Astoria hotel in New York to entertain world leaders including Obama, who are in the Big Apple to attend a series of high-profile meetings at the United Nations headquarters.
Hill sang I've Got the World on a String from the musical, which celebrates jazz icon Duke Ellington's years at Harlem's famous Cotton Club, while his co-stars performed Devil and the Deep Blue Sea and Creole Love Call - and the actor still can't believe he was asked to sing for the top politicians.
He tells the Associated Press, "I really enjoyed it. I never thought this would ever happen. If you'd have told me I was going to sing in front of all these dignitaries a month ago I would have laughed...
"It's not something that happens every day. When they asked me, it wasn't like I said, 'Well, let me check my schedule. I might want to watch the (American football) game.'"