Place a pork chop between two layers of plastic wrap on work surface. Using a meat pounder, pound to 1/4-inch thickness. Repeat with remaining pork chops. Transfer to a large resealable plastic bag or nonmetal container. Add balsamic vinegar and oil. Marinate, covered, in the refrigerator 15 minutes.
Meanwhile, heat a grill or grill pan to medium-high heat. Remove pork from marinade; season with salt and pepper. Grill until cooked through and browned on both sides, about 1 minute per side. Serve hot, garnished with basil and tomatoes.
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