Dogs, including shih tzu, by nature are predatory animals, and all predatory animals share the motivation to chase fleeing objects. While this may be a natural instinct, it is not appropriate when those fleeing objects are joggers, bicyclists or the mailman.
Training the shih tzu not to chase people and bicycles is an important thing to do, and it is best to start that training as early as possible. Starting when the shih tzu is still small and non-threatening is important, but particularly with breeds that grow very large, or with breeds that have a reputation for being very aggressive. Many people respond to being chased by a dog, especially a large dog, with understandable fear, and it is best for yourself and your shih tzu that he be trained not to chase.
Shih Tzu are probably easier to train away from chasing than others. Breeds that have been used for hunting or herding often retain much more of their chasing instincts than other types of dogs.
No matter what breed of dog you are working with, however, it is important to not allow him off the leash until his chasing behavior has been curbed. Allowing an untrained dog off the leash is dangerous, irresponsible and illegal.
Before you expose your shih tzu to a situation where he will want to chase someone or something, be sure to train him in a safe, controlled area like a fenced in yard. It is important for the shih tzu to be able to focus and concentrate on you, and for him to understand what behavior you want. The shih tzu must be given the opportunity to repeatedly perform the behavior you want while in this controlled setting.
The training session should be started indoors in the shih tzu