Preheat oven to 400 degrees F. In a 3-quart baking dish combine strawberries, vinegar, and jam. Sprinkle salt and pepper; set aside.
Cut a horizontal pocket in each chicken breast half by cutting from one side almost, but not through, to the other side. Cut Parmesan cheese in six 3x1/2-inch pieces. Wrap a basil leaf around each piece of cheese; stuff into chicken breast pocket. Secure pockets closed with wooden toothpicks or skewers. Sprinkle with salt and pepper.
In 12-inch oven-safe skillet cook garlic in oil over medium heat for 30 seconds. Add chicken and cook 5 minutes or until golden brown, turning once. Transfer to oven. Bake, uncovered, 5 minutes. Add baking dish with the strawberry-jam mixture to oven. Bake 10 to 13 minutes, or until chicken is no longer pink (170 degrees F) and the berries are softened and jam mixture has thickened. Serve chicken with melted strawberries. Sprinkle with basil. Makes 6 servings.