1. Combine blue cheese, celery, sour cream, and scallions in a bowl. Melt butter in 12-inch nonstick skillet over medium heat. Add chicken and hot sauce and summer until chicken is cooked through, 6 to 8 minutes. Transfer chicken mixture to bowl. Using 2 forks, shred chicken into bite sized pieces. Wipe out skillet.
2. Working one at a time, spread 1/4 blue cheese mixture over tortilla. Top with 1/4 chicken mixture. Top with second tortilla.
3. Heat oil in skillet over medium high heat until shimmering. Cook quesadillas until golden brown and crisp. Cut into wedges and serve.