
My last dog was terrible for chasing cats, luckily he was never as nimble as them and the closest he got to causing damage to one was getting a mouthfull of fluff as he snapped at the disapearing tail
(we never encouraged this behaviour, it was deeply ingrained when we got him as a rescue, but we were never good enough at training it out of him).
However, we got a kitten. When the kitten arrived it was kept seperate from the dog, the dog never even set eyes on it for the first couple of weeks. I would move the kitten around the house, in different rooms, so gradually the dog got used to the smell of the kitten allover the house and the kitten also took on the smell of us/our home.
After a couple of weeks, I'd bring the kitten into the room with the dog, but leave her in a pet carrier. Again just to get the dog used to her more.
Slowly the kitten was given more freedom and the dog never treated her the same as he did with strange cats, he treated her as part of the family. They got on great, they would even play together and sleep together.
It can work, but do remember a little kitten is not very good at getting out of trouble like an adult cat, so supervision for the kittens safety if very important.
If you are thinking of bringing in an adult cat, then supervision for your dogs safety is equally important - a cat scratch can cause the loss of an eye and can happen so very quickly.