...players of unknown skill can have an equal chance of winning...
This sounds like you want to take the player's skill out of the game which goes against the spirit and rules of chess, I would say. You could introduce elements that equalize skill differences but you may end up with a completely different kind of game, which you wanted to avoid.
For example you could introduce some kind of handicap or bonus (less time for the higher skilled, less chess pieces to begin with for the higher skilled, more chess pieces for the lower skilled (analogously to Go), other side tasks for the higher skilled) but that would require that you know the skill differences in advance or detect them while playing.
Please note, that winning chess for a lower skilled player because the higher skilled opponent had some kind of handicap is not the same as winning under otherwise equal conditions. In chess as most people play it, the definition of winning (in a statistical sense) means that you are higher skilled. Your definition of winning seems to be different (independent of skill). It would be a different kind of winning.
Indeed one could switch sides at random times as RemcoGerlich pointed out, and it would formally solve your problem, but in that case winning would be very much meaningless.
That's why I conclude that no, there is no such way. Either the stronger skilled players will win more often in chess, or the definition of winning becomes meaningless and some other kind of metric depends on the skill (like the handicap) or it's not standard chess any more.