Why Chows and cats are a case-by-case question
Some dog-and-cat pairings are easy because the breed was developed to work closely with people and other animals. The Chow Chow was not. Its background includes hunting and guarding, and many Chows retain a strong interest in chasing small, fast-moving animals. At the same time, Chows are not frantic dogs, and a calm adult Chow that grew up with a cat often treats that cat as part of its household and ignores other cats' existence indoors while still needing management outdoors. The individual dog's history matters more than the breed average here, so the honest answer for any specific Chow is found in its past behaviour around cats, not in a breed description.
The puppy route: raising them together
The most reliable path is a Chow puppy introduced to a cat from the first days at home, under supervision, with the cat always able to leave. Puppies learn household rules before their chase instinct matures, and a confident, dog-experienced cat that stands its ground teaches lessons no owner can deliver as clearly. Even then, supervision should continue for months, play should be interrupted before it becomes a chase, and the puppy should learn a strong recall and a settle command away from the cat. Never assume that a puppy who was gentle at twelve weeks will be equally gentle as a powerful adolescent, which is when many households get a surprise.
Introducing an adult Chow to a resident cat
With an adult dog, go slowly and use barriers before faces ever meet. Let the animals smell each other under a door and swap bedding for several days, then allow visual contact through a secure gate with the Chow on a lead, rewarding calm looking-away rather than fixed staring. A hard, unbroken stare, stiff body, and silence from the Chow are warning signs to increase distance, not progress to celebrate. Sessions stay short and end well. Only after repeated calm sessions should the dog be loose in the same room, and the cat must have high perches and a dog-free room it can reach at all times, protected by a gate or cat flap the Chow cannot follow through.
Reading behaviour honestly once they share a home
Owners often want the pairing to work so much that they explain away the early evidence. A Chow that fixates on the cat through the gate, trembles with excitement at movement, or has previously caught birds or squirrels is telling you the risk plainly, and management must then be permanent rather than a training phase: separate spaces when nobody is home, no unsupervised contact, and the cat's welfare given equal weight to the dog's. Plenty of households run that system successfully for years. What is not acceptable is hoping a high-drive dog will simply get used to a cat while loose together, because a single incident takes seconds and the cat pays for it.
Setting up a household where both animals can relax
Success looks boring: a cat who can eat, sleep, and reach a litter tray without crossing the dog's space, a Chow whose exercise and training needs are met so it is not looking for stimulation, and owners who keep feeding areas separate so the Chow's well-known protectiveness over food never has the cat as its audience. Feed the Chow behind a closed door if there is any guarding, and give the cat high, quiet territory of its own. KinsLe Circle of Love adds a wider local network of fellow pet owners around a household like this, so if a Chow ever gets loose there are more nearby people who know to look out for it.