Drain the chicken well and place in a bowl. Gently flake it with a fork. Stir in the salsa, cheese, and onion. Mix gently. Place half of the tortillas on a flat work surface. Top each evenly with some of the chicken mixture. Top the filling with the remaining tortillas. Heat a large skillet over medium heat. When hot, add one tortilla stack to the skillet. Cook for 2 minutes then gently flip the quesadilla over. Cook for 1-2 minutes longer or until the filling is heated through and the cheese has melted. Remove from the skillet and repeat with the remaining quesadillas. Serve the quesadillas hot with sour cream, guacamole, salsa, or any other desired condiments.