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