Mix the flour, salt and peppers in a shallow bowl.
Put the buttermilk in a small bowl.
Dip the chicken pieces into the buttermilk and then into the flour mixture one at a time.
Shake excess flour off and set the chicken on a wire rack while the oil heats.
Heat 1/2" of oil to about 350F in a deep skillet or electric skillet.
Lay the chicken pieces in the hot oil skin side down. Cook about 15 minutes. Monitor the oil--you may want to turn it down a little.
Turn the chicken pieces and cook another 15-20 minutes, until cooked through.
Take the chicken out of the frying pan and lay on a brown paper bag to drain. Let sit about 10 minutes before serving.