Two brilliant young aesthetes, Brandon Shaw and Phillip Morgan, strangle to death their former classmate from prep school, David Kentley, in their Manhattan penthouse apartment. They commit the crime as an intellectual exercise: they want to prove their superiority by committing the "perfect murder".
After hiding the body in a large antique wooden chest, Brandon and Phillip host a dinner party at the apartment, which has a panoramic view of Manhattan's skyline. The guests, who are unaware of what has happened, include the victim's father, Mr. Kentley, and aunt, Mrs. Atwater; his mother is unable to attend because of a cold. Also present are David's fiancée, Janet Walker, and her former lover, Kenneth Lawrence, who was once David's close friend.
Brandon uses the chest containing the body as a buffet table for the food, just before their housekeeper, Mrs. Wilson, arrives to help with the party.
Brandon and Phillip's idea for the murder was inspired years earlier by conversations with their prep-school housemaster, publisher Rupert Cadell. While they were at school, Rupert had discussed with them, in an apparently approving way, the intellectual concepts of Nietzsche's Superman, as a means of showing one's superiority over others. He, too, is among the guests at the party since Brandon, in particular, thinks that he would approve of their "work of art."
Brandon's subtle hints about David's absence indirectly lead to a discussion on the "art of murder." Brandon appears calm and in control, although when he first speaks to Rupert, he is nervously excited and stammering. Phillip, on the other hand, is visibly upset and morose. He does not conceal it well and starts to drink too much. When David's aunt, Mrs. Atwater, who fancies herself a fortune-teller, tells Phillip that his hands will bring him great fame, she refers to his skill at the piano, but he appears to think this refers to the notoriety of being a strangler.
However, much of the conversation focuses on David and his strange absence, which worries the guests. A suspicious Rupert quizzes a fidgety Phillip about this and some of the inconsistencies raised in conversation. For example, Phillip vehemently denies ever strangling a chicken at the Shaws' farm, although Rupert has seen Phillip strangle several. Phillip later complains to Brandon about having had a "rotten evening," not because of David's murder, but because of Rupert's questioning.
As the evening goes on, David's father and fiancée begin to worry because he has neither arrived nor phoned. Brandon increases the tension by playing matchmaker between Janet and Kenneth. Mrs. Kentley calls, overwrought because she has not heard from David, and Mr. Kentley decides to leave. He takes with him some books Brandon has given him, tied together with the rope Brandon and Phillip used to strangle his son. When Rupert leaves, Mrs. Wilson accidentally hands him David's monogrammed hat, further arousing his suspicion. Rupert returns to the apartment a short while after everyone else has departed, pretending that he has left his cigarette case behind. He asks for a drink and then stays to theorize about David's disappearance.
He is encouraged by Brandon, who hopes Rupert will understand and even applaud them. A drunk Phillip, unable to bear it anymore, throws a glass and accuses Rupert of playing cat-and-mouse games with him and Brandon. Rupert seizes Brandon's gun from Phillip and insists on examining the chest over Brandon's objections. He lifts the lid of the chest and finds the body inside. He is horrified and ashamed, realizing that Brandon and Phillip used his own rhetoric to rationalize murder. Rupert disavows all his previous talk of superiority and inferiority and fires several shots out the window to attract attention. As the police arrive, Rupert sits on a chair next to the chest, Phillip begins to play the piano, and Brandon continues to drink.
