Chester

From Memory Alpha, the free Star Trek reference.

Chester was the pet cat of Liam Bilby at his home on Farius Prime in 2374. After Bilby was killed during an operation for the Orion Syndicate, Miles O'Brien took Chester to Deep Space 9. (DS9: "Honor Among Thieves")

Later that year, Molly wanted to bring Chester with them on a trip to Golana. Keiko, who didn't particularly like the cat, feared that Chester may run away. (DS9: "Time's Orphan")

It is likely that when the O'Briens eventually left the station in 2375 for Earth, Chester moved with them, as he was part of the family now. (DS9: "What You Leave Behind")

Chester is the third of four recurring pets; the others were Livingston, Spot and Porthos.