Bring balsamic vinegar to a boil in a small saucepan over medium-high heat. Reduce heat, and simmer about 15 to 20 minutes or until reduced to 1/2 cup. Stir in 1 tablespoon butter; set aside.
Sprinkle both sides of scallops with salt and pepper. Heat remaining 2 tablespoons butter in a large nonstick skillet over medium-high heat. Add scallops, and cook 3 minutes on each side or until golden crust begins to form. Serve scallops with balsamic reduction dipping sauce.