http://en.wikipedia.org/wiki/World_Chess_Championship
... is that nobody has ever become world champion at a younger age than their twenties.
Being a chess idiot, I don't really know why this has been true, but I assume it's simply a matter of practice: that it takes time to get good enough at chess to usefully train against grandmasters, and then it takes time with the grandmasters before you can dominate at grandmaster-level chess, which my chessmaster friends have told me is almost like a different game, one which they can follow with great excitement but not necessarily understand well enough to play.