Start the grill or build a charcoal fire in the grill. Wash and dry the chops.
In a bowl, mix together all the ingredients for the rub. Spread the rub evenly over the lamb chops on both sides.
In a saucepan, combine all the ingredients for the balsamic reduction. Bring to a boil and reduce the heat to a simmer. Simmer for 10 minutes until the sauce thickens, stirring occasionally. Remove from the heat and remove the garlic and the rosemary.
Grill the chops over a medium fire (150 degrees F. internal temperature for medium-rare). When almost done, brush the chops on both sides with the balsamic reduction. Heat each side of the chops, remove to a platter, and serve.