The empirical answer is that white has some advantage. The historical results from grandmaster play are that white wins more often than black.
The game theoretic answer is presently unknown, but it's extremely likely that optimal play by both sides will result in a draw. If so, the first move advantage is a myth. Black probably has a narrower path to the draw though.
Is first move advantage in chess really just a myth? GM Andras Adorjan seems to think so!
http://ontheroadtochessmaster.com/review-of-black-is-back-by-andras-adorjan/