About one in every 10,000 chickens is gynandromorphous, to use the technical term.
In medieval times, they might have been burned at the stake, as witches' familiars.
But these chickens are shedding important new light on how birds, and perhaps reptiles, develop.
It used to be thought that hormones instructed cells to develop in male or female-specific ways.
That's what happens in mammals, including humans, and it leads to secondary sexual characteristics like facial hair for men or breasts for women.
But scientists at the Roslin Institute and the University of Edinburgh say they have discovered that bird cells don't need to be programmed by hormones.
Instead they are inherently male or female, and remain so even if they end up mixed together in the same chicken.
It means a half-and-half chicken will have totally different plumage, body shape, and muscle structure on the two halves of its body.
It even affects the wattles on the bird's head, and the spurs on its legs. They will be larger on the cockerel half, and smaller on the hen half, of the same bird.