If you purchase a show-quality Chihuahua, he should sport the classic apple dome skull. That's the American Kennel Club breed standard for Chis. While the apple-headed Chi is the only type that can compete in show ring conformation classes, there's also a deer-headed Chi who makes a perfectly fine pet. You can recognize deer-style Chihuahuas by the head shape.
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In most respects, standard, apple-domed Chihuahuas and deer-style Chis look much the same. They are the same size, appear in the same colors, have either short or long coats and possess similar temperaments. The current AKC Chi standard was approved in 2008. You can recognize the deer-style Chi by his longer, pointier muzzle and the greater slope of his forehead. The ears are longer than the apple-domed Chi.