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. (DS9: "Honor Among Thieves")
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. (DS9: "Time's Orphan")