Warm the chopped chicken briefly so it does not slow the melting of the cheese during cooking.
Place each tortilla on a flat surface and sprinkle a layer of cheese over one half.
Distribute the chicken over the cheese, add a small second layer of cheese, and fold the tortilla closed.
Heat a lightly greased skillet over medium heat and place one folded quesadilla inside.
Cook for 2 to 3 minutes per side until the tortilla is golden and the cheese has melted completely.
Rest for 1 minute, cut into wedges, and serve with tomato salsa, guacamole, or fresh lime.