One of the smallest dog breeds, chihuahuas often weigh as little as 4 lbs. or less. They are from the state of Chihuahua in Mexico, and have a colorful history. In spite of their diminutive stature, they often have big attitudes and display aggression towards people and other dogs and must be well-socialized before you can expect them to peacefully coexist with other animals, especially other dogs.
A member of the terrier family, pitbulls are perhaps best known as fighting dogs. This does not mean that all pitbulls fight, only that many breeders have selectively bred them for stamina and tenacity. Due to their reputation as mean dogs, many pitbulls that have been raised as family pets flood shelters every year. As with any dog, a properly socialized pitbull can be expected to live peacefully with other dogs if it has the personality to do so, although they may require a little more training than some other breeds.
Puppies learn social skills mostly in the puppy's first two or three months of life. It learns much of its social behavior from its mother and siblings. It may also be introduced into group situations by a responsible breeder and allowed to play and interact with other, unrelated animals. Dogs teach one another a lot about how to behave in different situations.
It is important to allow your pitbull and chihuahua to meet on neutral ground. Take them to a park or trail that is quiet and where neither has ever been before. Each dog should be leashed, and two different people should be responsible for the two dogs. Walk side by side, keeping the dogs parallel, and allow them to get to know one another in this way. When the dogs seem comfortable and neither is displaying any signs of fear or aggression, allow them to sniff one another, and continue with your walking. Once in the home, crate the dogs, or place them in separate rooms until you are certain they will get along. It is never advised to leave any group of dogs closed up together and unsupervised for too long, as pack behavior may take over and result in injuries to the animals.