On board an ocean liner bound for America, four stowaways—Chico, Groucho, Harpo, and Zeppo—hide in wooden barrels in the ship's cargo hold. After singing "Sweet Adeline," they are discovered and the ship's officers spend the rest of the voyage chasing and attempting to catch the mischievous quartet. Chico, Chico Marx, and Harpo, Harpo Marx, pose as barbers and shave off an officer's mustache while he is sleeping; Groucho, Groucho Marx, and Chico lock the ship's captain in a closet and eat his lunch; Groucho hides in the stateroom closet of gangster Alky Briggs and his wife, Lucille, Thelma Todd; Briggs leaves and Groucho begins romancing Lucille until he is caught and threatened by Briggs.
Briggs is so taken by Groucho's nerve that he hires both Groucho and Zeppo to cover him while he confronts Big Joe Helton, a rival mob boss, and gives them loaded guns, which they immediately ditch in a bucket of water. Chico and Harpo disrupt a chess game and confiscate the board, taking it into Helton's stateroom and Helton's daughter Mary, Ruth Hall. After they scare off Briggs during the confrontation with Helton, the mobster is impressed and hires Chico and Harpo to be his bodyguards. Groucho later offers his own protection services to Helton, who says he will think it over.
After the ship docks in the United States, the stowaways realize they need to steal passports to disembark. Zeppo swipes the passport of movie star Maurice Chevalier and demonstrates his ability to mimic the Frenchman's singing. The four cut in line at customs and Zeppo impersonates Chevalier. He is unsuccessful, however, and Chico, Groucho and Harpo, each attempt unconvincing portrayals of Chevalier singing, with Harpo resorting to strapping a phonograph on his back with an actual record of Chevalier singing. After a man faints, Groucho poses as a doctor and urges the crowd to gather around the unconscious man so he won't recover. Sailors remove the man from the ship on a stretcher, but it's actually the four stowaways hiding under a blanket.
Helton throws a coming-out party for Mary, whom Zeppo met and romanced onboard the ship. Groucho is reunited with Lucille at the party, where Chico plays piano and Harpo plays harp. Briggs' men, posing as musicians, kidnap Mary and hold her captive in an old barn. The four stowaways and Helton follow and Zeppo engages in fisticuffs with Alky Briggs, while Groucho delivers ringside commentary. Mary is rescued by Zeppo and Groucho attempts to find a needle in a haystack.
Except in the film's credits the Marx Brothers' characters have no names in this film. They are referred to simply as "the stowaways."
