COMBINE buttermilk, hot pepper sauce and 3 teaspoons salt in large resealable heavy-duty plastic bag. Seal bag and gently knead bag until salt is completely dissolved.
RINSE chicken; pat dry with paper towels. If necessary, cut into 2 breast halves, 2 thighs, 2 drumsticks and 2 wings. Cut each breast half in half, crosswise, for more even cooking. Reserve giblets and back for other use. Add chicken pieces to buttermilk mixture. Seal bag; turn to coat. Chill 4 hours or overnight, turning bag occasionally.
PLACE flour in wide shallow dish. Stir in baking powder, pepper and remaining 1 teaspoon salt. Remove chicken from buttermilk mixture, one piece at a time, shaking off excess. Add to flour mixture, turning to coat completely. Place coated chicken on wire rack set over a sheet of wax paper. Repeat to coat remaining chicken pieces. Let stand 15 minutes to set coating.
HEAT oil to 365°F in 12-inch deep heavy skillet or Dutch oven. Place half of the chicken pieces in hot oil, skin side down. Cover and cook over medium heat 6 to 8 minutes or until light golden brown. Turn chicken over and continue cooking, uncovered, an additional 7 to 11 minutes or until golden brown and internal temperature reads a minimum of 165°F. Reduce heat to medium-low if necessary to avoid overbrowning, but maintain a minimum oil temperature of 310°F. Drain on paper towels. Repeat to cook remaining chicken.