Sprinkle chicken with salt and pepper. Place chicken in a shallow dish or zip-top plastic bag, and add buttermilk. Cover or seal, and chill at least 2 hours.
Remove chicken from buttermilk, discarding buttermilk. Dredge chicken in flour.
Pour oil to a depth of 1 1/2 inches in a deep skillet or Dutch oven; heat to 360°. Add chicken, a few pieces at a time; cover and cook 6 minutes. Uncover chicken, and cook 9 minutes. Turn chicken; cover and cook 6 minutes. Uncover and cook 5 to 9 minutes, turning chicken the last 3 minutes for even browning, if necessary. Drain on paper towels.