Origin of Phrases - K
Keep it under your hat
Meaning: Keep a secret.
Example: Monica Lewinsky was told to keep it under her hat.
Origin: Back when men wore hats regularly, it wasn't unusual for them to put important things inside. To keep something under your hat was to keep it out of sight and shown to no one.
More probably, hats are worn on the head. "Keep it under your hat" is just a sly way of saying keep it in your head, to yourself.