Boil the rice for about 8 minutes, drain and set aside. The rice will continue to cook in the oven.
Season the lamb with salt, pepper, and 1/3 tablespoon of rosemary.
Heat the olive oil in a skillet over medium-high heat and brown the lamb chops for about 2 to 3 minutes per side (including the fat side).
When you pull the lamb out of the skillet, add the garlic and cook for about a minute just allow it to release some of its flavors.
Either in the skillet or in a tajine, mix the rice, tomatoes, balsamic vinegar, and rosemary.
Nestle the lamb into the rice mixture and sprinkle the olives around top of the rice. Cover with a lid.
In an oven heated to 325 degrees, cook the lamb and rice mixture for about 30 minutes or until the internal temperature of the lamb reaches about 145 degrees for medium-rare.