Wash chicken pieces and pat dry. Heat shortening about 1 inch deep in an electric skillet to 365 degrees.
Stir salt and pepper into flour and place in a shallow dish. Roll chicken pieces in seasoned flour and shake a little off. Roll again in flour mixture, then place in hot shortening.
Do this slowly, a couple of pieces at a time, so you don't cool down your fat. Do not crowd chicken pieces. The trick is to keep your shortening hot.
Turn chicken pieces every so often to brown evenly. Cook until the coating is a warm crispy brown. Remove the pieces that are done to a paper towel-lined platter and keep warm in a 180-degree oven while frying the rest of the chicken. Add more shortening if needed to keep it about 1 inch deep. Let it come up to temperature before adding more chicken.
Serve chicken on a platter piled high. Call everyone to the table as soon as the chicken is done so everyone can experience the aroma and warm goodness.