Place the chicken pieces in a large bowl and pour the buttermilk over them. Cover with plastic wrap and refrigerate overnight.

Preheat the oven to 350 degrees F.

Combine the flour, salt, and pepper in a large bowl. Take the chicken out of the buttermilk and coat each piece thoroughly with the flour mixture. Pour the oil into a large heavy-bottomed stockpot to a depth of 1-inch and heat to 360 degrees F on a thermometer.

Working in batches, carefully place several pieces of chicken in the oil and fry for about 3 minutes on each side until the coating is a light golden brown (it will continue to brown in the oven). Don't crowd the pieces. Remove the chicken from the oil and place each piece on a metal baking rack set on a sheet pan. Allow the oil to return to 360 degrees F before frying the next batch. When all the chicken is fried, bake for 30 to 40 minutes, until the chicken is no longer pink inside. Serve hot.