1In a small bowl or cup, mix together the rosemary, basil, thyme, salt and pepper. Rub this mixture onto the lamb chops on both sides. Place them on a plate, cover and set aside for 15 minutes to absorb the flavors.
2Heat olive oil in a large skillet over medium high heat. Place lamb chops in the skillet, and cook for about 3 1/2 minutes per side for medium rare, or continue to cook to your desired doneness. Remove from the skillet, and keep warm on a serving platter.
3Add shallots to the skillet, and cook for a few minutes, just until browned. Stir in vinegar, scraping any bits of lamb from the bottom of the skillet, then stir in the chicken broth.
4Continue to cook and stir over medium high heat for about 5 minutes, until the sauce has reduced by half. Unless you do so, the sauce will be runny and not good.
Remove from heat, and stir in the butter.
Pour over the lamb chops, and serve with steamed asparagus.