Pat the pieces of chicken completely dry with paper towels and season them on all sides with the salt and red pepper. In a heavy 12-inch skillet, heat the oil over moderate heat until a light haze forms above it.
Fry the chicken in the hot oil, starting the pieces skin side down and turning them frequently with tongs for about 20 minutes, or until they brown richly and evenly.
To be sure that the bird is cooked to the proper degree of doneness, lift a thigh from the pan and pierce it deeply with the point of a small skewer or sharp knife. The juice that trickles out should be clear yellow; if it is still tinged with pink, fry the chicken for 2 or 3 minutes more.
After all of the chicken pieces are cooked, drain them on paper towels. Then arrange them on a heated platter and drape them with foil to keep them warm.
Meanwhile, in another large heavy skillet, melt the butter over moderate heat. When the foam subsides, add the mushrooms and, stirring occasionally, cook for 5 minutes, or until the mushrooms are tender and the liquid that accumulates in the pan has evaporated. Do not let the mushrooms brown. Remove the pan from the heat and reserve the mushrooms.
When the chicken has cooked its allotted time and been transferred to the platter, pour off all but about 4 tablespoons of the fat remaining in the skillet and in its place add the flour; mix well. While stirring constantly with a wire whisk, pour in the chicken stock in a slow, thin stream and cook over high heat until the sauce comes to a boil, thickens heavily and is smooth. Reduce the heat to low and simmer for 2 or 3 minutes to remove the raw taste of the flour.
Stir in the mushrooms, olives, sherry and artichoke hearts, and simmer for a minute or so longer to heat them throughout.
Taste for seasoning, then ladle the sauce and vegetables over the chicken and serve at once.