Dogs chasing cats is part of pet ownership. Some dogs may chase cats because they see them as a form of prey, others because they see them as potential partners in play. Regardless of why your dog is chasing cats, you will want to put a stop to it quickly. Your dog can accidentally injure or kill a cat, or the cat could injure your dog. Consulting an experienced behaviorist or trainer to compile a training plan for your dog's needs is always a good idea.
Provide Plenty of Exercise
Boredom and excess energy can get your dog looking for something to do. If you take him on vigorous walks, trips to the dog park and obedience exercises, he is less likely to harass a cat. Exercise doesn't prevent all bad behavior, but you should look hard at your dog's activity level when he picks up annoying or dangerous habits. Running him out of energy on suitable-length jaunts will leave him too tuckered for the tabby.
Teach With Timeouts
Decide ahead of time on a particular room, such as the bathroom, for a timeout. As soon as you notice your dog fixate on the cat, calmly tell him, "Timeout," attach a leash to his collar, and walk him to the timeout room. Leave him in the room for a minute or two, then let him out. Repeat the process every time he fixes his gaze on the cat. Ideally, you will catch him before he actually chases the cat, but that isn't always possible. Do not yell at your dog, jerk on his leash or otherwise punish him. Remain calm and nonemotional while working with him.
Reward Good Behavior
Keep small treats handy all the time, so you can quickly reward the dog when you catch him being good. Ignoring the cat when it enters the room, paying attention to you rather than the cat, and other calm, nonaggressive behaviors deserve a treat.
When your dog stops chasing your cat, thanks to your reinforcement, it can be easy to let your guard down. But it is important to supervise him until he has proven he is reliable. Gradually extend the period of time you leave the two unattended, from just leaving the room for a few minutes to leaving them alone in the house together. Just because your dog comes to understand that he cannot chase your cat doesn't mean that he knows he cannot chase any cats. If loose cats live in your neighborhood, keep your dog on a leash outside, and continue your treat training, until he reliably ignores those as well. Remember, every circumstance is different; even if he ignores strange cats while out on walks with you, he may feel different if he sees one in what he considers his territory.