The Enterprise is called to Deep Space Station K7 by Undersecretary Nilz Baris to protect a shipment of quadrotriticale grain. Captain James Kirk is frustrated by Baris's use of a high-priority distress call for a minor issue and begrudgingly complies. The Enterprise crew enjoys shore leave on the station, as does the crew of a Klingon ship led by Captain Koloth.

Interstellar trader Cyrano Jones arrives with merchandise, including fluffy, purring creatures called tribbles. He gives one to Lt. Uhura, who takes it on the Enterprise. The tribbles reproduce rapidly on the ship and station, enchanting the crew, even Spock. Unfortunately, however, they react negatively to Klingons.

A brawl between humans and Klingons erupts when a drunken Klingon insults the Enterprise and its crew. Kirk cancels shore leave, and Baris fears Klingon's interference with the grain project, suspecting Jones of being a Klingon agent.

Dr. McCoy and Spock worry that the growing number of tribbles could consume the ship's food supply. Kirk realizes the tribbles on the station might endanger the grain shipment. Upon investigating, he finds many dead or dying tribbles, suggesting the grain has been poisoned.

Baris blames Kirk for the disaster, while Koloth demands an apology from Kirk for his crew's mistreatment. Their arguments are interrupted when the tribbles react to Baris's assistant, Arne Darvin, revealing him as a disguised Klingon. Darvin admits to poisoning the grain.

Jones is instructed to remove the tribbles from the station or face charges for transporting dangerous life forms. However, before the Klingons leave, Chief Engineer Scott transports all the tribbles onto the Klingon vessel, ensuring "they'll be no tribble at all."