New research has shown that Core Vaccines are necessary for Chow and Shih Tzu Puppies. Typical recommendations for scheduling Core Vaccination are for a first vaccine on or about 8 weeks, followed by a booster at 16 weeks. This should provide your puppy with lifetime immunity.
Before vaccinating your puppy more than this, ask your vet about performing a Titer test (VacciCheck) to see if your dog already has immunity.
Vacine-induced diseases will shorten your dog's life.