Não foi durante as filmagens de Caddyshack, mas durante o Saturday Night Live. Murray começou no Saturday Night Live no outono de 1977. Chevy Chase havia deixado o show no final da temporada de 1977 e seu filme "Foul Play" estava previsto para ser lançado em meados de 1978. A luta aconteceu em 18 de fevereiro de 1978. De acordo com o excerto do livro "Live from New York", blog, Bill Murray afirma:
"I got into a fight with Chevy (Chase) the night he came back to host. That was because I was the new guy, and it was sort of like it was my job to do that. It would have been too petty for someone else to do that. Its almost like I was goaded into that. I did sense that. I think they resented Chevy for leaving, and leaving and making his own career go. Everybody else was from the improvisational world, where you don't make it about you. You were an ensemble, you were a company. So when he left, there was resentment about that. It was a shock.
"At the same time, Chevy was the big potato on the stew. He got the most sketches, he had the most influence, he got the publicity -- all of those things. So they didn't miss that part of it. But there was still hangover feelings that he shouldn't have left until everybody had that. You make sure everybody else is there and then you do it.
"It did leave a big vacuum, because he was really heavy in those shows. You look at those early shows and he's heavy. And so you had a whole year when the writers ended up writing, like writers do -- they write for the guys who can get it done, who can get it on the air -- and Chevy's sketches got on the air because he was "the man," you know. The other actors had to start from scratch and teach the writers how to write for them ... When you become famous, you've got a year or two where you act like an asshole. You can't help yourself. It happens to everybody. You've got, like, two years to pull it together -- or it's permanent.
De acordo com o membro do elenco Laraine Newman
"It seems that there was a tension between Chevy and Bill all along during the week. I don't know why. I don't know if Chevy provoked it or not. But it culminated with Billy saying to Chevy, 'why don't you fuck your wife once in a while?' And I don't even remember who threw the first punch, Billy or Chevy. But it was ugly. I'd never seen guys fighting like that, let alone people I knew. And, you know, I don't know how he did it, but Chevy went out and did the monologue a few minutes later. Watching from the floor, he seemed shattered.
De acordo com a Seção do IMDB Caddyshack Trivia , a cena com o personagem de Murray e Chase no greenskeeper shed não estava em o roteiro original. Harold Ramis percebeu que os dois não tinham cenas juntos em todo o filme, então ele sentou-se com Murray e Chase e trabalhou na cena.