Spray 13x9-inch (3-quart) glass baking dish and 16x12-inch sheet of foil with nonstick cooking spray. Heat large nonstick skillet over medium-high heat until hot. Add chicken; cook 3 to 4 minutes or until chicken is no longer pink in center, stirring frequently. Remove from heat. Stir in soup, sour cream and chiles.
Spread 1/4 cup of the enchilada sauce in sprayed baking dish. Arrange half of the tortilla pieces over sauce, overlapping as necessary. Spoon and spread 1 cup enchilada sauce evenly over tortillas. Spread half of chicken mixture over sauce. Top with 1 cup of the cheese. Repeat layers, starting with tortilla pieces. Cover tightly with sprayed foil. Refrigerate at least 8 hours or overnight.
Heat oven to 375°F. Bake covered 30 minutes. Uncover baking dish; bake an additional 20 to 25 minutes or until sauce is bubbly and cheese begins to brown. Let stand 15 minutes before serving. Sprinkle with onions.