1. In a medium saucepan, cook shredded chicken, barbecue sauce, and diced green chiles over medium heat until heated through.
2. Coat one side of each tortilla with cooking spray. Place tortillas, sprayed sides down, on cutting board or waxed paper. Sprinkle 1/4 cup of the cheese over half of each tortilla. Top evenly with shredded chicken mixture. Fold tortillas in half, pressing gently.
3. Heat a large nonstick skillet over medium heat. Cook quesadillas, two at a time, in hot skillet over medium heat for 4 to 6 minutes or until light brown, turning once. Remove quesadillas from skillet; place on a baking sheet. Keep warm in a 300 degree F oven. Repeat with remaining quesadillas. To serve, cut each quesadilla into three wedges. Serve with salsa, sour cream, and green onion. Makes 4 servings.