It wasn't during the filming of Caddyshack but during Saturday Night Live. Murray started on Saturday Night Live in the fall of 1977. Chevy Chase had left the show at the end of the 1977 season and his movie "Foul Play" was due to be released in mid 1978. The fight took place February 18, 1978. According to the excerpt from the book "Live from New York", on this blog, Bill Murray states:
"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.
According to cast member 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.
According to the IMDB Caddyshack Trivia Section the scene with Murray and Chase's character in the greenskeeper shed were not in the original script. Harold Ramis realized that the two had no scenes together in the entire movie so he sat down with Murray and Chase and worked out the scene.