Preheat the oven to 350 degrees and grease a 9 by 13 inch baking dish.
Cut the chicken into strips about one inch thick for faster cooking, if desired. Add the olive oil to a large skillet, and heat over medium. Add the chicken strips and sprinkle with salt and pepper to taste. Cook for 3 to 4 minutes on each side, or until the internal temperature reaches 165 degrees. Shred the chicken, or dice it into small pieces.
Place the cooked chicken pieces in a bowl, and stir in the diced green chilis.
Warm the tortillas in a covered casserole dish in the oven while you prepare the other ingredients (about 10 minutes). Alternately, you can microwave 4 tortillas at a time between 2 slightly damp paper towels for 20 seconds (or until soft). This will make them easier to roll.
Add beans, cooked chicken, enchilada sauce, and cheese to the center of each tortilla (about 1 ½ to 2 tablespoons of each ingredient). Roll each tortilla, then place it open side down in the greased 9 by 13 inch baking dish. Once all the filled tortillas have been arranged in the pan, spread the remaining cup of enchilada sauce over the tortillas, then sprinkle with the remaining cup of cheese.
Bake uncovered for 10 to 15 minutes, or until the enchiladas are heated and the cheese is melted.