1. Gently pound the chicken breasts between sheets of plastic wrap with a flat meat mallet or a rolling pin until 1/3-inch thick.
2. Whisk together buttermilk, hot sauce, 1/2 teaspoon salt, and black pepper in a shallow dish, then add chicken, turning to coat, and let stand 15 minutes.
3. Stir together bread crumbs, cayenne pepper, and remaining 1/2 teaspoon salt in another shallow dish.
4. Remove chicken from buttermilk one piece at a time, letting excess drip off, then dredge in bread crumbs, pressing gently to help them adhere. Transfer chicken as coated to a sheet of was paper.
5. Heat oil in a 10-inch heavy skillet over moderately high heat until hot but not smoking, then fry chicken 2 pieces at a time until golden brown and cooked through, about 3 minutes on each side. Transfer chicken with tongs to paper towels to drain and serve with hot sauce on the side. Serve with crunchy Iceberg and Watercress Salad with Blue Cheese Dressing. (See recipe here.)