This article is from the Chihuahua Breed FAQ, by firstname.lastname@example.org (Melinda 'Bob' Casino) with numerous contributions by others.
If they have their American Kennel Club official certificate papers,
yes--they can run up to $600.00. The papers (which the breeder
provides) mean that the parents of your Chi are registered with the
AKC and that the puppy is registerable. Additionally, some breeders
provide pedigree papers which trace the family history beyond the
immediate parents. These papers are vital if you plan to enter your
new dog into exhibitions and competitions.
These certificates and papers ensure that the dog is a purebred;
however, I hasten to add that just because a dog has papers, doesn't
mean it qualifies for exhibitions and competitions. (See AKC
Chihuahua Breed Standards.) At the least, the papers will ensure that
your Chihuahua has come from a responsible breeder.
Chihuahuas who do not have their papers are not significantly
different than those with papers. Moreover, they can be bought for
much less. (I bought mine for $200.00 without papers.)