Heat 1 tablespoon of the Rosemary Olive Oil in large skillet over medium heat.
Add onions and cook until reduced by half and beginning to turn golden in color, about 5 minutes. Add garlic, a bit of salt and pepper. Stir until fragrant, about 30 seconds.
Add blueberries, 1/4 cup water, and balsamic vinegar. Stir to blend.
Mash berries with the back of fork and cook until sauce thickens, stirring often, 3 to 4 minutes. Let stand at room temperature.
Brush grill rack with oil. Turn grill to medium-high heat. Brush lamb chops on both sides with oil; sprinkle with salt and pepper. Grill about 3 to 4 minutes per side for medium rare. Transfer to plates. Spoon sauce over the meat. Serve immediately.