Heat olive oil in a large flying pan over medium heat. Add chopped onion and garlic and cook until soft and lightly brown. Season with salt and pepper. Add Balsamic vinegar, chicken broth, and honey in the skillet.
Turn to high and heat just until boiling. Turn heat down to medium-low and simmer until liquid is reduced to half. Stir in butter and let it melt. Turn off stove and let ingredients blend together.
Wash and dry chicken thoroughly. Trim off excess fat if any. Pound chicken down to about 1/2 inch and place in a 9X13 baking pan. Add Balsamic liquid to chicken, cover with foil and bake at 350 Degrees for 40 minutes. Uncover chicken and add a small can of black olives drained.
Recover and continue baking for 10 more minutes or until chicken is done. Olives will blend in the balsamic juices just enough to pick up the flavor and still remain firm.