Pat lamb chops dry and arrange in a single layer in a shallow glass baking dish.
Whisk Dijon mustard, balsamic vinegar, garlic, and pepper together in a small bowl. Whisk in oil slowly until marinade is smooth. Stir in basil. Pour marinade over lamb chops, turning to coat both sides. Cover and refrigerate for 1 to 4 hours.
Bring lamb chops to room temperature, about 30 minutes.
Preheat grill for medium heat and lightly oil the grate. Grill lamb chops until browned, 5 to 10 minutes per side. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).