As far as dog behavioral problems go, chasing can be one of the most dangerous. Your dog could end up chasing something into the street. Your dog may end up getting into trouble, or even lost, by chasing something you don't want him or her to, or by getting out of your range. Many methods work, from remote training to leashes, but the specific one you use will depend on the breed as well as your efforts.
Dogs chase as a natural part of their genetic makeup. To curb this behavior, you have to give your dog a reason to stop. In the case of hunting dogs, you also need to teach them when it is okay to chase and when it isn't. Remote training usually works best in such situations.
Sometimes you just need to distract your dog from whatever it is he or she wants to chase. You can do this by making a noise with a clicker, using a training collar, or by being active with your dog in some other way. When in public, it is always best to keep your dog on a leash for safety as well as legal liabilities.
When training your dog without a leash, first distract your dog and then offer him or her positive reinforcement when behaving well and not giving chase. It really is that simple. Remember that your dog is a pack animal and you are the pack. Your dog looks to you for affection and protection. His or her sole purpose is to take care of the pack and retain his or her place in it. This is why positive reinforcement is so effective.