Combine chicken, vegetable oil, and cayenne pepper in a bowl; let stand at least 15 minutes, or longer if desired.

Preheat the oven to 325 degrees F (165 degrees C).

Heat a skillet over medium-high heat. Add chicken mixture; cook until no longer pink. Remove from heat; set aside.

Meanwhile, spread a thin layer of tortilla chips in a 9x13-inch baking dish; top with 1/4 chicken, 1/4 chiles, and 1/4 cheese. Repeat layers three more times ending with cheese.

Bake in the preheated oven until cheese melts and nachos heated through, 15 to 20 minutes. Serve with your favorite nacho toppings.