Heat oil in a deep-fryer or large saucepan to 190 degrees C. Combine the bread crumbs, Parmesan cheese, garlic salt and pepper in a bowl; set aside.
Place the mayonnaise and chipotle chillies into a blender and puree until smooth. Scrape the mayonnaise mixture into a plastic bag; add the chicken breasts and coat evenly with the mayonnaise. Press the chicken breasts into the bread crumb mixture and shake off any excess.
Cook the chicken breasts in the hot oil until the breading is golden brown and the breasts are no longer pink on the inside, about 8 minutes.