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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 350ºF.
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 360ºF 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 360ºF 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.