In a small bowl whisk together the rosemary, basil, and thyme. Rub the mixture into the lamb chops on both sides and then sprinkle with salt and pepper to taste. Cover and let stand for 15 minutes.
In a large skillet over medium-high heat cook the chops until well browned on one side, flip the chops and continue to cook to desired doneness. (Medium rare 145F. Medium well 160F.)
Remove chops from skillet, set aside on a serving platter, and cover with aluminum foil to keep warm.
Add the shallots to the skillet and cook until they start to brown. Stir in the Balsamic vinegar and chicken broth stirring to remove any bits from the bottom.
Continue to cook over medium-high heat until the sauce is reduced to 1/2 or less, and then stir in the honey. Serve the sauce hot over the chops.