In a large bowl, combine the chicken and sauce, and stir until evenly coated. Add the cheese and toss to combine. Evenly divide chicken mixture on 6 tortillas and top with remaining 6 tortillas.
Heat a large skillet over medium heat and coat with nonstick cooking spray. Cook the quesadillas, one at a time, about 3-4 minutes per side, using a spatula to turn. Cut into quarters and serve with blue cheese dressing and celery sticks on the side.