Heat oil in a large skillet over med-high heat. Cook chops for about 4 min per side for med-rare or continue cooking to desired doneness. Remove from skillet & keep warm on serving platter.
Add shallots to skillet, cook for a few minutes until browned. Stir in balsamic, scraping any bits of lamb from the bottom. Continue to cook about 5 min, until sauce has reduced by half. Remove from heat and stir in butter. Pour mixture over chops & serve.