Dogs can easily kill cats. Sometimes you need to make a safety zone where dogs are not allowed and cats are, until you can train your dog.
Take your dog to an obedience class. Make sure it really learns to come when called, obey you, and drop things when you give a command. Chasing cats is not okay and should not be allowed. In your home, put the dog on a leash before letting the cat into the area the dog is allowed into. If it begins to chase the cat, correct it by the collar every time, saying a command like "leave it!". Be commanding but not mean, let it know you mean business. If your dog has a strong prey drive, it could take a very long time to train it. It might be safer to find a new home for your cat, just don't take it to the humane society, find a home yourself.
And no matter what you do, don't let a dog like this roam or get loose or you will have some very upset neighbors!
Dog/cat rescue volunteer/vet hospital employee