The best way to handle this is to slowly allow your Chihuahua to become accustomed to cars. It may not seem logical that your dog is afraid of cars; however think for a moment how large and scary a car may seem to such a tiny dog as the Chihuahua!
You should begin by going for a relaxing walk in a very quiet neighborhood. If you do not live in such an area, you can drive to one. Or you could find a quiet park that allows dogs. Quite frankly, the Chihuahua is so small that many owners go for walks in "Non-dog" parks.
Keep your Chihuahua close to you and speak in a matter-of-fact voice as you slowly walk. Be sure to not use a soothing tone, as this can signal to a dog that his owner is trying to provide comfort in response to a real threat. If a car does approach, your dog will look to you for clues in regard to behavior
Do not act panicked and pick up your dog. Simply talk calm and tell your Chihuahua that everything is okay. Continue walking; Do of course, stay on the sidewalk. If there is no sidewalk, you should be closest to the street and allow your dog to walk on the inside.
Any time that a few minutes goes by with the dog remaining calm, alternate between giving praise and giving a small treat.
Many owners give up on the first few tries; they do not want to put their dog through a stressful situation. However, by starting off in an area of low traffic, ignoring fear based behavior and rewarding tolerance for traffic, a dog can learn that his fear has no basis.
Your Chihuahua will slowly get used to these types of walks and then you can take it up a notch by going to a more crowded area. Again, if any cars go by or you see any other dogs, stay calm and speak with a casual tone. Dogs can sense emotion even if you do not say anything, so do not tense up. Depending on the puppy or dog, it can take a week to several weeks for fears of the outside to subside.