Melt 1 tablespoon butter in a large skillet. Add shallots and cook over medium heat for 5 minutes or until very soft, stirring frequently. Add Amazin Diced Prunes and cook for 5 minutes more.
Make a horizontal slit in each chicken breast to form a large pocket. Place equal amounts of onion mixture and a piece of cheese inside each breast and secure with toothpicks; season with salt and pepper. Brown chicken in remaining butter on both sides. Tent with foil and cook for 10 minutes over low heat, turning once or twice.
Stir together preserves and vinegar and pour over chicken. Cook for 10 to 15 minutes more or until chicken is cooked through and sauce is slightly thickened. Remove toothpicks and top with snipped fresh basil.