Sprinkle chicken with salt and pepper and place chicken in a shallow dish or zip-top plastic bag, then add buttermilk. Cover or seal, and chill for at least 2 hours.
Remove chicken from buttermilk; discard buttermilk immediately. Dredge each piece of chicken in flour.
Pour vegetable oil to a depth of 1 1/2 inches in a deep skillet or Dutch oven; heat to 360°. Add half of the chicken; cover and cook for 6 minutes. Uncover chicken and cook for 9 minutes. Turn chicken over; cover and cook for 6 minutes. Uncover and continue cooking for 5 to 9 minutes, turning chicken the last 3 minutes for even browning, if necessary. Drain chicken on paper towels. Repeat with remaining chicken. Let cool for 10 minutes before serving.