In a large skillet, melt butter or margarine and add olive oil. Saute garlic and onion until translucent. Remove garlic and onion from skillet with a slotted spoon.
Add chicken breast halves to skillet and brown on both sides. Return garlic and onion to skillet. Add broth and bourbon and stir all together. Cover and let simmer over very low heat for 20 to 25 minutes, or until chicken is tender and done (chicken juices run clear).