Chester
Chester was the pet cat of Liam Bilby at his home on Farius Prime in 2374. According to his owner, Chester had a favorite chair and didn't like it when someone else sat in it. 

When "Connelly" (aka Miles O'Brien) admitted that he found Morica Bilby's cake to be dry, Liam remarked to Chester about the man's honesty. 

Later, he fed Chester.

Upon discovering O'Brien's true identity, Bilby asked him to look after Chester. After Bilby died during an operation for the Orion Syndicate, O'Brien brought Chester to Deep Space 9. The cat seemed to take to him, leaping onto O'Brien's lap. ()

Later that year, Molly wanted to take Chester with them on a trip to Golana. Keiko, who didn't particularly like the cat, tried to sway her from the idea. Miles added that he might get lost, which changed Keiko's mind about taking the cat.

While there, Molly expressed her interest to be an exobiologist, which she defined as "someone who studies animals from other planets", prompting Keiko to give Chester as an example. Molly then asked if she could take Chester with her should Miles send his wife and daughter away from the station again. Miles assured her he wouldn't send them away again. ()

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Cats