The leg was more likely amputated--a good surgeon can make it look like the leg was never there at all, especially once a few years have passed since the surgery. I have a cat whose leg was amputated when she was a kitten and most people who see her assume she was born that way. The only tip off is a small place where the tabby markings don't completely line up, but you wouldn't even have that on an animal with solid coloring.

As long as the rest of his legs are ok, he should get along fine! Couldn't hurt to get him checked out by a vet to make sure he doesn't have any orthopedic problems, though, especially since patellar luxation is pretty common in Chihuahuas. It's a knee problem that can be corrected best if you catch it early on.