Trek's Pets: all named and recurring pets in Star Trek
Chester - O'brien's cat - Star Trek: Deep Space Nine
One of the most underappreciated aspects of Star Trek: Deep Space Nine is the way they could do genre episodes... because we were out of the purview of the Federation a lot of the time, a gangster episode taking place in the lawless galactic frontier made perfect sense. Ironically, despite going where no Star Trek episode had gone before, the problem with DS9's gangster episode "Honour Among Thieves" was unoriginality; the plot was a beat-for-beat retelling of the classic Donnie Brasco.
...and a little formulaic. Screenwriter Blake Snyder coined the term "saving the cat" to describe an action taken by the hero or a sympathetic character that tells the audience to root for them. The tragically doomed sympathetic gangster Al Pacino..., I mean Liam Bilby had a cat named Chester that O'Brien adopts after Bilby is killed by the Orion Syndicate.
Chester appears once more in an episode that's equally strange but is more original. "Time's Orphan" hangs together much better than "Honor Among Thieves," and involves Molly O'Brien wandering off during a family picnic, falling into a time portal, and returning as a teenage feral child. Molly had been a non-entity up until that point (not her fault, there's just generally very little for an eight-year-old to do on a space station that's ground zero for a pan-galactic clash of civilizations.) But "Times Orphan" requires us to care about her. It requires us to miss the happy-go-lucky little girl we hardly knew. We need to know Molly to feel what the O'Briens feel as they come to terms with their daughter being a mute animalistic teenager. So we start with a scene of Molly excitedly bonding with Chester.
That scene is also a rare glimpse of mundane family life on DS9, reminding us that the station is not just the setting for fantastical sci-fi tales and high-stakes diplomacy, but a place where civilians and families live. It was one of those scenes that effortlessly packs in a lot of information. It's good storytelling.
Chester did for Molly what he did for P̶a̶c̶i̶n̶o̶ Bilby, telling us who she is.