Is there a way to make chess an absolutely fair game?
We can run a pair of games, sequentially, where player one first plays white, then black.

Let's write W for win, L for lose and D for draw, from the point of view of player one. In the cases WW,WD,DW, player one wins the match. In the cases LL,LD,DL, player one loses the match. In the cases WL,LW,DD, the match is a draw.
(If a draw match is undesired, play another match.)