The Chi-Chi is a cross between a Chinese Crested and a Chihuahua. Dogs. Chi-Chis are known as hybrids or cross-breeds. Sometimes they are called designer dogs to differentiate them from mixes of unknown heritage. The chi-chi is a small dog who is known to take part in competitive obedience and agility sports, They are characterized by a rectangular-shaped body along with an apple or wedge-shaped head like their Chihuahua or Chinese Crested parents. Chi-Chis have bright, round or almond shaped eyes, a slightly arched neck that appears long and slim, narrow shoulders, slender and straight legs as well as a C-shaped tail that is curved when the chi-chi is excited.