Place the chicken pieces in a large bowl and cover with the buttermilk; set aside, covered and refrigerated, for several hours or overnight.
Place the flour, salt and pepper in a large paper or plastic bag.
Remove the chicken from the buttermilk, shaking off any excess.
Working in batches of 2 or 3 pieces, place chicken in the bag and shake until coated with the flour and seasonings.
In a large skillet, over medium-low heat, heat the oil.
Fry the chicken, working in batches, if necessary, and turning the pieces often, 20 to 30 minutes, or until golden brown on all sides.
Remove from skillet and place on a plate covered with paper towels prior to serving.