Heat olive oil in a large nonstick skillet over medium-high heat.
Sprinkle lamb loin chops with salt and pepper.
Add lamb to pan, and cook 3 minutes or until browned. Turn lamb over, and cook 4 minutes or until desired degree of doneness.
Remove lamb from pan; keep warm.
Add chopped onion and garlic to pan; cook 3 minutes or until onion is tender.
Add wine; bring to a boil. Cook 3 minutes or until liquid evaporates. Stir in broth and balsamic vinegar; bring to a boil. Cook 2 minutes or until reduced to about 2/3 cup.