In a medium bowl, combine shredded cooked chicken with buffalo sauce. Stir until chicken is evenly coated.

Lay one tortilla flat. Sprinkle about 1/4 cup of cheese over one half of the tortilla. Spoon about 1/2 cup of the buffalo chicken mixture over the cheese. Top with another 1/4 cup of cheese.

Fold the empty half of the tortilla over the filling to create a half-moon shape.

Heat a large non-stick skillet or griddle over medium heat. Add olive oil or butter. Place the quesadilla in the hot pan.

Cook for 3-5 minutes per side, or until golden brown and crispy, and the cheese is melted and bubbly. Press down gently with a spatula.

Transfer cooked quesadilla to a cutting board. Let rest for a minute, then slice into wedges.

Serve immediately with ranch or blue cheese dressing, and celery/carrot sticks if desired.