Season lamb chops with rosemary, basil, thyme, salt, and pepper.
Heat olive oil in a large skillet over medium-high heat. Place lamb chops in the skillet, and cook for about 3 minutes per side for medium-rare, or to your desired doneness. Remove from skillet, and keep warm on a serving platter.
Add shallots to the skillet, and cook for a few minutes, just until browned. Stir in balsamic vinegar, scraping any bits of lamb from the bottom of the skillet, then stir in chicken broth. Continue to cook and stir over medium-high heat for about 5 minutes, until the sauce has reduced by half. Remove from heat, and stir in the butter. Pour over the lamb chops, and serve.