The hippodrome was an open space designed for horse and chariot races. One of their ends had a semi-circular shape so that the chariots could easily change the direction. The length of a hippodrome is usually greater than the length of a stadium. During the Roman Empire often hippodrome and stadium denoted the same space.
Most famous are the hippodromes in Olympia and the one Emperor Constantine built near his palace in Constantinople (which no longer exists).