Preheat oven to 350F.

In medium bowl, combine flour, salt and pepper. Coat chicken well with seasoned flour. In large heavy skillet, heat olive oil and butter over medium-high heat. Add chicken breasts to skillet and saute for 2 minutes on each side, just until golden. Remove chicken to casserole dish, arranging in single layer.

Add onion, garlic and ginger root to the skillet; cook 1 minute. Stir in apple slices. Blend in cider, brown sugar and vinegar. Simmer on low heat 4 to 5 minutes. Pour mixture over chicken and bake for about 20 minutes. Remove from oven, serving at once. (If sauce does not thicken into glaze, remove chicken to plates and stir 1 teaspoon flour mixed with 3 tablespoons cider into casserole dish. Cook and stir over medium heat, just until thickened. Spoon over chicken and serve.)