In a large sauce pot, combine chicken and 5 cups water. Bring to a boil, reduce heat and cook until chicken is very tender, approximately 20 minutes. Remove chicken and let cool. Reserve 1 ½ cups stock for use in casserole.
Coat a large skillet with nonstick cooking spray. Add butter or margarine and onion; saute onion until golden. Add canned soups, green chiles, 1 ½ cups chicken stock, and cooked chicken. Set aside.
Coat a 9 x 13-inch baking pan with nonstick cooking spray. Pour 1 cup of chicken mixture on bottom of cooking pan before assembling casserole. To assemble casserole, place tortilla on a place and then place approximately 2/3 cup chicken mixture in the center of tortilla with 2 Tbsp cheese, roll the tortilla up and place in casserole dish. Repeat this for each tortilla while equally distributing ingredients until all tortillas are placed in casserole dish. Drizzle remaining sauce and cheese over tortillas. Cover with foil and bake at 350 degrees until bubbly, approximately 45 minutes. Let stand 10 minutes before serving. Makes 10 servings.