Chihuahuas shake because they are cold, nervous, excited or have excessive energy. In rare circumstances, tremors can indicate medical conditions such as hypoglycemia or an allergic reaction. However, the most common cause for shivering in Chihuahuas is falling temperatures. Since they are small, they are more susceptible to cold temperatures.
Dogs who have recently been introduced to new surroundings or people often shiver because they are excited or nervous. Additionally, Chihuahuas are very high-energy dogs, which may cause them to shake even when they are snug and in familiar surroundings. Since shivering is common in this breed, it's usually nothing to be alarmed about unless it's out of character for an individual dog.