Trim, wash, and dry the chicken livers. Cut them into halves. Sauté the livers in the butter and season with salt and pepper. Cook over high heat, shaking the pan frequently so the livers do not stick. Do not overcook; the livers should be tender, but not dry.
Sprinkle the livers with the flour, add the shallots, shake the pan, and let cook for one-half minute.
Add the stock and bring to a boil, stirring gently. Add the parsley, wine and additional salt and pepper to taste.