Rinse wings and pat dry. Place in Pyrex dish. Pour buttermilk over chicken pieces, turn all pieces to coat well. Cover and marinate in refrigerator for 3-6 hours.
Preheat oven to 400 F. Retrieve wings from marinade and place in large mixing bowl. Toss wings in a generous amount of Franks hot sauce, saturating each piece well.
Place wings on a rack inside a baking pan (so fat can drip off). Bake for about 50 minutes (baste with more hot sauce halfway through) and then shake them up in more hot sauce, to taste.
Serve with blue cheese dressing and celery sticks.