Chihuahua puppies can go home at 8 weeks at the earliest, but with smaller breeds like Chihuahuas, the longer the puppy stays with it's mom and siblings, the better it will be for that puppy later in life. With larger breeds, it's ok for them to go to new homes at 8 weeks old. Responsible breeders will not sell their puppies if they are a Toy Breed, until they are at least 12 weeks old. This is the time that they learn certain behaviors from their mom, that will give them better temperaments later in life. I used to breed Chihuahuas and I never let any of my puppies that were adopted out, go to their new homes, until they were at least 12 weeks old.
Usually recommended 12 weeks but may take at 10 weeks the soonest since baby chihuahuas are more tinier
My best friend got her chihuahua at 2 months old. She loves her like family.