While a single individual can't be named as chess' inventor, an ancient legend an old fable that is not to be taken literally names Grand Vizier Sissa Ben Dahir as the game's originator.
The father of modern chess is generally considered to be Wilhelm Steinitz, who was the first official World Chess Champion in 1886. However, the origins of chess itself can be traced back to ancient India, where it was known as chaturanga.