According to Eris, Kurill Prime was the homeworld of the Kurillians, which was conquered by the Dominion in 2370. However, Eris was not a Kurillian but a Vorta spy, so at least part of her story was a fabrication. (DS9: "The Jem'Hadar")
Background information Edit
This planet was only mentioned in dialogue.
According to the script, the pronunciation for Kurill was "kuh-RILL". 
According to Star Trek: Star Charts (p. 71), Kurill Prime was the homeworld of the Vorta. This Class M world was where the Changelings discovered the Vorta as the small, timid, ape-like forest dwellers. They originally were, living in hollowed-out trees to avoid predators. Changelings genetically engineered the Vorta into intelligent humanoids and employed them at the highest level of the Dominion, as the story was told in DS9: "Treachery, Faith and the Great River".