Preheat oven to 400 degrees F. In a 3 qt. baking dish combine strawberries, vinegar & jam. Sprinkle with salt & pepper; set aside.
Cut a horizontal pocket in each chicken breast half by cutting from one side almost, but not enough through, to the other side. Cut cheese in 6 - 3 x 1/2" 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 & pepper.
In 12" oven-safe skillet cook garlic in oil over medium heat for 30 seconds. Add chicken & 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 - 13 minutes, or until chicken is no longer pink (170 degrees F) & the berries are softened & jam mixture has thickened. Serve chicken with melted strawberries. Sprinkle with fresh snipped basil.