What was the name of the space station in 'The Trouble with Tribbles'?

The space station in “The Trouble with Tribbles” was Deep Space Station K-7. The USS Enterprise is summoned there after Undersecretary Nilz Baris issues a high-priority distress call to protect a shipment of quadrotriticale grain bound for Sherman’s Planet.

K-7 quickly becomes the center of a comic crisis when the trader Cyrano Jones brings tribbles to the station. One tribble given to Lieutenant Uhura reaches the Enterprise, where the creatures reproduce at astonishing speed. The station’s public areas, storage compartments, and grain shipment soon become overwhelmed.

The station also hosts Klingon visitors under Captain Koloth, creating friction between the Klingons and the Enterprise crew. A poisoned grain shipment exposes the hidden identity of Arne Darvin, a Klingon agent. The title is often remembered simply as “the tribble station,” but K-7 is the canonical name; it is not Station K-5, Starbase 11, or a place on Earth.