Breeding a Chihuahua and a Great Dane naturally is impossible due to the significant size difference between the two dogs. While artificial insemination can technically make it possible, it is risky for the mother's life. There is no evidence of successful breeding between these breeds, and it is not recommended. Instead, people can consider other mixed breeds like Pomsky, German Shepherd Corgi, or Pitbull Dachshund. Chihuahua Great Dane mixes should not be bred due to ethical and medical concerns.