2. Peel and slice the onions 1/2" thick. Rub the onion slices (trying to keep them intact) with the olive oil and sprinkle with salt and pepper.
3. Grill the onions until they are lightly charred and cooked through, about 3 to 4 minutes per side.
4. When the onions are cool enough to handle, chop them roughly and put them in a bowl. Add the balsamic vinegar. (This can be stored in the refrigerator for up to 1 week.)
5. Prepare the Tomato Vinaigrette.
6. Season the lamb chops with salt and pepper and grill for about 4 minutes on each side.
7. Rewarm the tomato vinaigrette.
8. To serve, spoon the onion relish on warmed plates and place 2 lamb chops on the relish. Top with about 2 tablespoons of the tomato vinaigrette.