I "had" Chelsea on a flight from Aspen to Denver. It was a quickie. I had boarded already, in row 3F if I recall correctly. On walked two secret service guys and kicked out the passengers sitting in 3A and 3C. I think the passengers had just sat in those seats and hadn't been assigned them. Then in walked Chelsea and her boyfriend at the time. (This was probably 1997).
I'm a straight man but the boyfriend was an objectively decent looking guy. Chelsea is not necessarily the prettiest, objectively speaking (don't want to offend anyone). I guess that proves Kissinger's theory that power is the ultimate aphrodesiac. (sp?).
This doesn't really count since it wasn't on a United flight but it was part of a United run: I was in Rio for a day and a half this May with my brother on a run and, while hanging out with a friend of my brother who lives in Rio, the friend ran into a friend of his. The guy turned out to be an extremely (and I mean extremely) famous Brazilian television star. His name is Zeca Camargo. He hosts Brazil's version of Survivor and Big Brother, along with a Sunday night show watched by 80 million people. We hung out with him for a while and had lunch with him both Saturday and Sunday. We even strolled up the beach at Ipanema with him. People were coming up asking for his autograph, his picture, etc. It was really bizarre because the guy was just incredibly famous but to me and my brother, who hadn't heard of him from Adam's off ox, he was nobody special. And by nobody special, I mean, he wasn't famous to us. But he was incredibly nice, not just to us but to all of his fans. It was a really cool experience.