In a medium bowl, stir together the chicken, vegetable oil, and cayenne pepper. Let stand for 15 minutes, or longer if desired.
Heat a skillet over medium-high heat. Add the chicken mixture, and fry until chicken is no longer pink. Remove from heat, and set aside.
Preheat the oven to 325 degrees F (165 degrees C). Spread a thin layer of tortilla chips in a 9x13 inch baking dish. Sprinkle 1/4 of the chicken, 1/4 of the chilies, and 1/4 of the cheese over the chips. Repeat layers ending with cheese on the top.
Bake for 15 to 20 minutes in the preheated oven, until the cheese is melted and everything is heated through. Serve with your favorite nacho toppings.