Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
In the bowl of a food processor, combine the balsamic vinegar, garlic, and honey. Pulse until blended. With the machine running, slowly pour in the vegetable oil until the mixture is smooth and forms a thick sauce. Season with salt and pepper, to taste.
Season the lamb chops with salt and pepper. Drizzle with the olive oil and sprinkle with rosemary. Grill the lamb chops for 2 to 3 minutes each side until medium-rare.
Arrange the lamb chops on a platter. Spoon the sauce over the top or serve the sauce on the side.
Recipe courtesy of Giada De Laurentiis, 2008