Although it may seem part of their nature, you can train a dog not to chase cats. This is a guide about training a dog not to chase cats.
Here are questions related to Training a Dog Not to Chase Cats.
By AndieL from Bristol, PA
How do I stop my dog from chasing cats?
By Bonnie J from Prineville, OR
Our dogs have responded fairly well to the "Leave It" command when they begin to bother the cats. That only works when we are present to give the command. After a while they might cease in their attempts to bother cats. Our cats mainly live in the large finished basement w/ their own private picture window, so don't feel sorry for them, they are quite content. Sometimes the dogs are just curious & sniff the cats or want to play w/ them. It might help to give the dog plenty of attention in the presence of the cat, or pay attention to them simultaneously if you can. There is some valuable info on the internet related to this topic.
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