Melt 1 tablespoon butter and heat olive oil in a large skillet over medium heat. Season chicken with salt and pepper, and brown on both sides in the skillet. Cover, and continue cooking 10 minutes, or until chicken juices run clear. Set aside, and keep warm.
Mix shallots and garlic into skillet over medium heat, and cook until tender. Stir in wine, and cook until heated through. Stir in broth, and continue cooking 5 minutes, or until reduced and slightly thickened. Mix in the remaining butter until melted. Serve the sauce over the chicken.