The first Marx Brothers movie, The Cocoanuts, was released May 2, 1929. It was a movie version of their stage play of the same name and included some of the same cast members, including Groucho, Harpo, Chico and Zeppo Marx and Groucho's frequent straight-woman, Margaret Dumont. The movie was set in Florida during the hotel boom with Groucho and Zeppo (the family straight man - and quite handsome) being the managers of the hotel and the other brothers doing, um, other things.
According to Joe Adamson, the brothers were so appalled by the final version of the movie, they tried to buy the negatives from Paramount so they could burn them. It's a good thing they didn't because the movie earned nearly two million dollars in profit!
An interesting tidbit: since they couldn't digitally remove unwanted sounds at that time, the sound techs soaked every bit of paper that was used as a prop so they wouldn't make crinkly sounds.
The Cocoanuts - Wikipedia
The Cocoanuts - Internet Movie Database