Preheat oven to 200 degrees F. Pound out chicken to 1/4 inch thickness. Season flour with salt and pepper and dredge chicken. Warm oil and 1 Tbsp. butter in large skillet over medium-high heat until butter foams. Add chicken and cook until browned, about 4 minutes. Turn and cook until firm and browned on both sides, about 3 minutes longer (or until cooked through). Place chicken on platter in the oven to keep warm.
Add Worcestershire sauce, vinegar and broth to empty skillet and bring to a boil, scraping up browned bits from bottom of pan with a wooden spoon. Boil, stirring occasionally, until thickened, about 5 minutes. Remove from heat and stir in remaining 1 Tbsp. butter until melted. Season sauce with salt and pepper.