Heat the shortening in a large cast iron or other heavy skillet over medium-high heat.
In a brown paper lunch bag combine the flour, salt, and pepper. Shake two chicken pieces in the bag to coat, and place them in the skillet. Repeat until all of the chicken is coated and in the skillet.
Fry the chicken over medium-high heat until all of the pieces have been browned on both sides.
While the chicken is browning, preheat the oven to 375 degrees. Once chicken is browned, remove it to a shallow roasting pan with a flat rack in the bottom. Bake for 30 to 40 minutes, or until chicken pieces are a deep golden brown and the juices run clear.