Rib chops can be costly. This exact same preparation works well on lamb loin chops, too.
4 garlic cloves, finely sliced
1/2 cup finely chopped rosemary
1/4 cup olive oil, plus more for sprinkling
12 lamb rib chops (about 2 1/4 pounds total)
Kosher salt, freshly ground pepper
1 pound cherry tomatoes, preferably on the vine
Integrate garlic, rosemary, and 1/4 cup oil in a large bowl. Working one at a time, pound lamb chops in between 2 sheets of plastic wrap to about 1/4″ thick; cut any excess fat. Season with salt and pepper and add to marinade; rely on coat. Cover and chill a minimum of 2 hours and up to 1 day.
Prepare a grill for medium-high heat. Get rid of lamb chops from marinade and rub out marinade. Grill lamb chops, turning often and moving around on grill as needed, till charred on both sides, about 3 minutes. Transfer to a plate.
Drizzle tomatoes with oil; season with salt and pepper. Grill in a grill basket or large cast-iron skillet up until lightly charred and blistered, about 4 minutes.
Serve tomatoes together with lamb.