The only part of the body that has no blood supply is the cornea in the eye. It takes in oxygen directly from the air.
The cornea is the transparent outer layer of the eye that helps to focus light onto the retina. Because it needs to be clear for light to pass through, it does not have any blood vessels. Instead, it receives oxygen directly from the air and nutrients from the aqueous humor, a fluid that fills the front chamber of the eye.
Other parts of the eye, such as the iris and sclera, do have blood vessels. However, the cornea is unique in that it does not require a blood supply to function.