Scare as Hen's Teeth

Etymology:

• This expression originated in the 19th century in America. Earlier the phrase was expressed as “scarcer than a hen’s tooth” which originated from a chicken pen, where hens are kept. It is noticing that hens do not have true teeth. To grind the food they eat, they have gizzards for that purpose. Since this is a distinct feature of hens that they don’t have teeth that simply suggest it to be a rare thing. Similarly the phrase means to suggest any thing that is nonexistent.