The Big Bad Wolf
To start at the very beginning– yes, I'm going pretty far back– all dogs descended from the wolf species. Yup, our little Chi's came from wolves.
It may seem hysterical, that our little 4 pound, round-headed, short-haired Chihuahuas came from a 100 pound, cunning hunter, capable of bringing down animals twice its size. Regardless, some where back in time, the transition from wolf to domesticated dog to Chihuahua happened– just keep in mind it didn't happen overnight.
Dogs are a descendant from the family called Canidae. There are two categories of this family– either wolves or foxes. Genetic testing confirms that dogs began their direct dissension from the wolf side– from the Grey Wolf to be exact– and did so 135,000 years ago.
Where as, genetic testing on foxes tell us they began their own separate species nearly a million years earlier. All this means is that dogs and foxes have been so far apart on the family scale for so long that the best you could say is that they are very distant cousins.
The fact that some Chis have a fox-like appearance doesn't mean they were bred with foxes. It just pays tribute to the fact that they have the same ancestral background.
With all that said, I did a little more research on wolves and found that this could very easily be where the Chihuahuas inherited their pack mentality, desire to stalk and rush after birds, and their innate ability to retrieve. Perhaps, too, this is where they get the feisty attitude and willingness to take on dogs triple their size.