Place the chicken pieces in a large bowl. Pour buttermilk over them, add half the salt and pepper, and toss to coat. Chill for at least 2 hours, preferably overnight, for best results.
Heat oil in a deep fryer or pot to 350–375°F (175–190°C). Fry chicken in batches for 12–15 minutes until golden brown and the internal temperature reaches 165°F (74°C).