Nilz Barris
William Schallert

Captain Koloth
William Campbell

Cyrano Jones
Stanley Adams

Mr. Lurry
Whit Bissell

Korax
Michael Pataki

Arne Darvin
Charlie Brill

Admiral Fitzpatrick
Ed Reimers

Ensign Freeman
Paul Baxley

Sherman's planet is a world of strategic importance that has been claimed by both the Klingons and the Federation for colonisation. Under the terms of the Organian peace treaty, ownership will go to the side that can prove the most effective use of it. The Enterprise is approaching Deep Space Station K-7, the nearest Federation outpost to the planet, when it receives a priority one emergency signal from the station that signifies near total disaster and, possibly, a Klingon attack.

However, when the ship arrives there is no sign of trouble and Kirk receives a call from the station manager, a Mr. Lurry, apologising for the signal and requesting Kirk to beam over. Spock and Kirk transport to the station where Lurry tells them that the man responsible for the Sherman's planet project, Nilz Baris, ordered him to make the call. They are introduced to Baris and his assistant, Arne Darvin, who try to command Kirk to post security guards on a store of high-yield grain called quadrotriticale, which is bound for Sherman's planet, as they are afraid that the Klingons might try to destroy it.

Kirk is furious with them but is calmed down by Lurry who persuades him to post the guards and offers his crew shore leave facilities. Uhura and Chekov encounter an interstellar trader by the name of Cyrano Jones in a bar and Uhura eventually ends up acquiring a tribble, a small furry animal that coos in a relaxing way when she holds it. Kirk receives orders from Admiral Fitzpatrick to assist Baris in any way possible and, only minutes later, the Enterprise detects a Klingon vessel approaching. By the time Kirk can contact the station a Klingon captain, Koloth, is already in Lurry's office.

The Klingons insist on their right to use the shore leave facilities and are told by Kirk that only twelve at a time will be allowed on the station, each one monitored by a security guard. On his return to the Enterprise he finds the recreation room infested with tribbles that seem to multiply at a fantastic rate. Kirk visits McCoy who has examined the creatures and is told that they are practically born pregnant. Simply feeding them is enough to make them reproduce. In the bar on the space station Jones tries to sell the Klingons a tribble but it screams loudly whenever a Klingon gets near it.

One of the Klingons starts to insult Kirk and Scotty has to hold Chekov back to keep things calm. However, when the Klingon starts to insult his beloved Enterprise it is just too much for Scotty to bear and a knock-down drag-out brawl begins which has to be sorted out by security, after which all shore leave is cancelled. Kirk confines Scotty to quarters, which is ideal for the engineer as it gives him the opportunity to catch up on some technical journals. Gradually, the Enterprise becomes completely overrun with tribbles and Kirk goes across to the station to see if the same thing is happening there.

When the grain storage bins are checked, thousands of tribbles pour out all over him. All of them are extremely gorged and completely dead. - it seems as if something must be wrong with the grain. McCoy is put on the case while Jones receives a summons to Lurry's office from Kirk. Koloth bursts in on them to make an official complaint. The tribbles that Jones is carrying react loudly to his presence and the trader is asked to leave the room. On the way out he bumps into Arne Darvin and the tribbles go berserk. Jones explains that the tribbles do not like Klingons and Kirk gets McCoy to scan Darvin.

It turns out that the grain was purposely poisoned and that Darvin is a Klingon agent. Koloth and his crew are given six hours to leave Federation territory. Cyrano Jones is told by Kirk that, in order to avoid arrest, he has to collect every tribble on K-7. On his return to the Enterprise Kirk is pleasantly surprised to find no tribbles, but no-one is prepared to tell him exactly what has happened to them. Eventually, Scotty admits that it was his doing and that, just before the Klingon ship went into warp, he 'transported the whole kit and kaboodle into their engine room where they'll be no tribble at all'.