Craig Claiborne believed a cast-iron skillet to be essential for the authentic preparation of this dish.
Sprinkle the chicken on both sides with salt and pepper. Select a skillet large enough to hold the chicken comfortably when it is opened up, as for broiling. Fold wings under to secure them.
Melt the butter in the pan and add the chicken, skin side down. Cover chicken with a plate that will fit comfortably inside the skillet. Place a heavy can, stone or brick on top of the plate to weigh it down. Cook over low heat, checking the chicken skin, until it is nicely browned, about 25 minutes.
Remove weight and plate. Turn chicken so skin side is up. Replace plate and weight and continue cooking for about 15 minutes more.
Remove chicken and pour off fat from the skillet, leaving about 2 tablespoons in the pan. Add the flour to the fat, stirring with a wire whisk over medium heat.
Gradually add the chicken broth and, when thickened, return chicken to the skillet, skin side up. Add salt and pepper to taste. Cover with the plate and weight and continue cooking over low heat about 20 to 30 minutes longer or until the meat is exceptionally tender. Spoon the sauce over it.
Cut chicken into serving pieces, and serve with the sauce and fluffy rice on the side.
