Some here have stated that white has a one-move advantage, which is certainly incorrect.
White has a half-move advantage. It is true that before each black move, white is ahead one move. However, after each black move, equal moves have been made by each side. Averaging all decision points in the game yields a .5 move advantage.
Also, it is easy to see that there are a number of ways to give up a move immediately in most real-world games, if having it were not actually an advantage.
If we take a simple example of a mirrored game, where black attempts to duplicate every move of white's, white will rapidly be ahead material. You could argue that being ahead material is not an advantage in some configurations, but having the choice to take that material, having more control of the outcome, certainly is.
You might find the previous concept absurd, but let's look at it from another perspective. Given every possible exactly mirrored board position, it seems intuitive that more of them would be mate-in-one for the first to move. (I have not done this calculation, but it would be an interesting and probably achievable search to run.) If we broaden this to all possible configurations, it seems intuitive that mate-in-one would on-average be more accessible to the first to move. Etc. And we need not follow this trail too deeply, either. Forced mate-in-six is a challenging find for most humans.
Many people have played many games of chess, some without any preconceived notions. If a clear way to neutralize white's opening advantage with certainty had been played, it would be well-documented by now. In fact, much opening strategy exists in chess surrounding this concept. See chess "tempo".
In endgames a well-known concept is zugzwang, where a clear disadvantage exists to having to move. However, this disadvantage exists because of the lack of choice, not because of having first choice; the move a player must make is disastrous (or more accurately the disaster has already occurred). Reiterating tbischel's comment, chess may never be solved by man. Because of this, we play games forwards, rather than backwards, as humans - and because of THAT, having the first move is an advantage.