Heat the oven to 375°F and grease a 9-by-13-inch baking dish.
Stir the chicken, beans, corn, green chiles, cumin, salt and pepper together in a large bowl.
Spread 1/2 cup enchilada sauce in the dish, then layer half the tortillas, half the chicken mixture, 1/2 cup sauce and 3/4 cup cheese.
Repeat the layers and finish with the remaining sauce and cheese.
Cover with foil and bake for 20 minutes, then uncover and bake for 10 to 15 minutes more, until bubbling and 165°F in the center.
Rest for 10 minutes before cutting so the tortilla layers settle.