A games of chess with perfect play from both sides may be a draw. And while we don't have any perfect chess players it does seem that a match between two equally strong grandmasters is more likely to be drawn that a game between two equally strong amateurs (though I have no statistics on this).
I believe the closest thing we have to perfect play is world-class correspondence play. Are top quality correspondence games yet more likely to be drawn that OTB grandmaster games?
EDIT in response to @Rauan's question: I'm not sure whether world-class correspondence play allows for use of computer, but I would be interested in statistics either way.
EDIT: in response to @Spork's point engine vs. engine games, I looked around online. The CCRL list shows the strongest AIs drawing 45%-60% of the time at relatively brisk 40-moves-in-40-minutes time controls. I found a post on chess.org that says that human grandmasters "have a draw rate approaching 60% or more in their games with other GMs," but these would be at longer time controls than the 40/40. So I don't think there's a clear signal.
A site called KCEC has a regression analysis showing that stronger engines to tend to draw more than weaker engines even when correcting for the difference in rating between opponents.