Place chicken breast halves in a shallow baking dish; pour Marsala wine over the chicken breasts. Refrigerate for 1 to 2 hours. Remove chicken from wine marinade; sprinkle with salt and pepper. Return marinade to refrigerator.
Heat butter and olive oil over medium; add chicken breast halves. Cook for about 5 minutes on each side, until chicken is browned, tender, and juices run clear. Transfer chicken to serving dish; cover and keep warm. Add reserved marinade and the halved grapes to skillet. Cook and stir until mixture boils. Continue to boil for about 45 seconds. Pour over chicken. Serve with rice and a vegetable side dish.