Yes, I know... "everyone" has an Aunt or Grandmother who has or had a Chihuahua and all that dog ever did was bark . It is true. A Chihuahua is really a Rottweiler stuck in a five pound body, so they have a lot to complain about; however, I find that with a little bit of training and some understanding you can easily teach your Chihuahua not to bark....too much!
I recommend that all dog owners purchase the book titled The Dog Whisperer by Paul Owens. I got this book for Christmas from my mother (who is not particularly fond of my barking friends), and have found it to be quite amazing. The book explains how to train a dog to do all sorts of things through positive reinforcement. For example, when your dog is barking, say “speak”, and reward the dog. Rewarding is best done with a clicker (a clicker is a common training tool that makes a small clicking noise when pressed) and a treat, then once they are able to bark on cue, you teach them to be quiet by saying “quiet”. I have implemented this over the past 3 weeks with my dogs - they still bark at people who come over, but I am able to quickly quiet them, all with a word and a click. What good is a dog anyway if they don't render the door bell completely useless?
It is also important to socialize your puppy as much as possible. Invite friends over; ask them to stop by as much as possible, take your dog to work, to the park, to Petsmart, wherever you can. The more a dog is used to the less they have to bark about.
Mostly, I have come to the conclusion that because Chihuahua are so little and cute, their owners do not find it necessary to spend the time training them. If you put the time into it you will be amazed at the abilities that these small friends possess.