Under one’s hat

To keep something under one’s hat is to keep something secret or confidential, away from public scrutiny, and dates in this sense from the late 19th century. The expression is American in origin and may have derived from earlier, literal instances of hiding papers or valuables under one’s hat. Hats in those days were certainly large enough for this to be possible and there is a story that Abraham Lincoln used to keep some of his papers under his famous black stovepipe hat.