Chester is the pet cat of the Orion Syndicate operative Liam Bilby, who asks Miles O'Brien to take care of the animal before going to his death, and who then lives with the O'Briens.
Chester first appears in the sixth-season episode Honor Among Thieves. He belongs to Liam Bilby, a minor member of the Orion Syndicate on Farius Prime, whose organisation O'Brien infiltrates for Starfleet Intelligence. The cat is one of the small domestic details that make O'Brien like the man he is there to betray.
When Bilby learns the truth and chooses to walk into a fatal ambush rather than bring the Syndicate's revenge on his family, his last request is that O'Brien look after Chester.
O'Brien takes the cat back to Deep Space 9, and Chester is seen again in the family's quarters in Time's Orphan.