Cut each chicken breast into 2 to 3 pieces. Pound the chicken about 1/4 inch thick between sheets of waxed paper with a meat mallet. Coat the chicken with a mixture of the flour, 1/2 teaspoon salt and 1/4 teaspoon pepper. Drain the artichokes, reserving the marinade. Heat the reserved marinade and olive oil in a saute pan over medium heat. Brown the chicken lightly in the olive oil mixture in the pan. Spoon the chicken into a 9x13-inch baking dish, reserving the pan drippings. Add the butter to the reserved drippings. Heat until the butter melts. Stir in the mushrooms.
Saute for 3 minutes. Remove the mushrooms to a bowl. Add the undrained tomatoes, garlic, 1 teaspoon salt, oregano, basil and 1/4 teaspoon pepper to the saute pan. Simmer for 10 minutes, stirring occasionally. Pour the tomato mixture over the chicken. Drizzle with the sherry. Bake at 350 degrees for 15 minutes.
Add the artichokes and olives to the mushrooms and mix gently. Add the artichoke mixture to the chicken mixture and mix well. Bake for 10 minutes longer or until bubbly. Spoon over hot cooked brown or white rice. May be prepared in advance and stored, covered, in the refrigerator. Bring to room temperature and bake as directed.
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