Chihuahua cheese (Queso Chihuahua) was a cheese made by the American Mennonites and was taken to Mexico by the missionaries. The cheese is similar to a mild cheddar and in fact cheddar makes a reasonable substitute. The best Chihuahua cheese is produced in Mexico and is still hard to find in the U.S. although there are U.S. produced products. Use Chihuahua cheese for melting in chiles rellenos or in queso fundido (a Mexican fondue).
If you are fortunate enough to have a good local Mexican market then that would be the first place to look. Kroger markets as well as Gelson's, Walmart and Costco are listed as seller's of Supremo brand Chihuahua cheese.
If you don't have or can't find Chihuahua cheese then here are the best two substitutes: