The length of a Chihuahua's coat is determined by two genes. The smooth coat gene is DOMINANT (indicated by capital letters), and the long coat gene is RECESSIVE (indicated by lower case letters).

The dominant smooth coat gene, if present, will completely hide the recessive long coat gene. So, a dog can be a smooth coat (the dominant gene is expressed, or seen), and have a hidden long coat gene, which it can pass on to the offspring.

Genetics of Coat Length by Michele Giroux with thanks to Fidelma Dixie, Pat Whitter & Carol Pyrkosz

Vetgen offers a coat length determination DNA test.

Coat Length
From: http://www.vetgen.com/canine-coat-color.html

"While it is not a color trait, the length of a dog's coat is of interest to many. It has recently been demonstrated that in many breeds, the gene FGF5 is responsible for whether a dog has a long coat (rough or fluffy), or a short (smooth) coat. The test Vetgen offers detects the presence or absence of the recessive allele that results in long coats when present in two copies, and as such allows dogs with short coats that carry a hidden "long coat" allele to be detected."