Chewing on things is completely natural to a dog. Dogs chew to clean their teeth, exercise their jaw muscles, and for entertainment and relaxation. Dogs, and especially puppies, explore their environment with their teeth. Your Chihuahua has many good reasons to chew, and with mouths that tend to be small and sometimes crammed with too many teeth, chewing may be even more important for your Chihuahua than for other breeds.
Chihuahuas, like most tiny breeds, are prone to teeth that do not match up evenly, which can lead to plaque buildup and decay, as well as jaw issues from uneven grinding. These problems can lead Chihuahuas to chew on things of different shapes and textures, so as to compensate for any issues with their jaws and teeth. This is why Chihuahuas will sometimes chew on strange things even late into life, and even if provided with chew toys.
Since chewing is a natural behavior for a dog, it is impossible to teach your Chihuahua not to chew at all. Rather, you must teach her the concept of your things and her things, which is which, and what is appropriate behavior with each. It may not ever be possible to trust your Chihuahua completely with free rein of your house, especially since the tiny Chihuahua may chew something dangerous like electrical cords or wood furniture, which can splinter and lodge in tiny throats. It is, however, reasonable to expect your Chihuahua to restrain herself at least while you are home.
Chihuahuas are sensitive animals capable of learning not just what is theirs and what is ours, but what is the appropriate sort of behavior with various sorts of toys. For instance, your Chihuahua can learn that while she is allowed to play with her stuffed toys by biting and carrying, she is not allowed to chew holes into them and pull out all the stuffing.
Unquestionably, the most important tools available to you in teaching your Chihuahua not to chew on your things are things your chihuahua is supposed to chew on. Pet stores are full of products ranging from natural antlers, horns, and hooves to hard and soft plastics. Chew toys come in all shapes and sizes, flavored and unflavored, edible or indigestible. Many can be stuffed with food treats, or frozen or microwaved for the added element of being hot or cold. Do your research and have fun buying as diverse a field of chew toys for your Chihuahua as you can afford. Don’t skimp on larger toys either, little dogs often love settling down with a huge bone to work on for hours from every imaginable angle. Do be careful of very hard, weight-bearing bones, as these can quickly wear down little teeth.
Another useful tool to have at your disposal is a bitter taste spray. It is best to buy a couple of varieties so you can be sure of finding one that your dog does not like. Be very careful in applying these sprays to furniture or fabric, as they can be damaging.