Combine 3 cups of buttermilk, salt, and sugar in a large resealable plastic bag.
Add all chicken pieces to the brine; seal bag. Chill overnight.
Drain chicken; pat dry with paper towels. Discard brine.
In a large bowl, combine flour, and 1/4 teaspoons each of salt and pepper. Place 3/4 cup buttermilk in a shallow dish. Coat chicken with flour mixture, dip in buttermilk; coat again with flour mixture.
Meanwhile, heat peanut oil in large skillet or Dutch oven to depth of 1 1/2 inches and 350 degrees.
Using tongs, carefully add a few pieces of chicken at a time to skillet. Maintain oil temperature at 325 degrees. Fry chicken for 12-15 minutes or until no longer pink, and coating is golden brown, turning once. Drain on paper towels. Keep fried chicken warm in a 300 degree oven while frying remaining pieces.