adv. phr. , informal 1. Without waiting; immediately; promptly. If you need a babysitter quickly, call Mary, because she can come at the drop of a hat.
Compare: ON THE SPUR OF THE MOMENT. 2. Whenever you have a chance; with very little cause or urging. At the drop of a hat, he would tell the story of the canal he wanted to build. He was quarrelsome and ready to fight at the drop of a hat.