Heat oven to 400°F. Line large cookie sheet with foil; spray with cooking spray.
In large bowl, mix 1/2 cup of the cooking sauce, the chicken, 3/4 cup of the cheese and the chiles. Divide chicken mixture among tortillas; sprinkle with remaining cheese. Fold tortillas over filling. Place on cookie sheet.
Bake 8 to 9 minutes or until tortillas are light golden brown, filling is hot and cheese is melted. Meanwhile, in 1-quart saucepan, heat remaining cooking sauce until hot; serve with quesadillas as a dipping sauce. Serve quesadillas whole or cut into wedges. Serve with salsa, sour cream and guacamole