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It'd be chaotic, yes, but fuck it.
1. Players flip a coin to decide who sort of goes first.
2. The player who sort of goes first makes a move for White.
3. The player who sort of does not go first then decides whether to play Black or White.
4. Play proceeds normally with the Black player.
This is called the "pie rule" in reference to the tradition of "whoever divides the pie gets the last pick of slices". This puts the burden on the first player of creating an opening position with 50/50 odds.
The "pie rule" is a convenient solution to a very common strategy game flaw. It is not, in my mind, a satisfying solution - it's a patch over a design flaw that often deserves some extra thinking - but, well, Sovreign Chess has it, which sort of patches out the Obviously Strong Opening problem.
(Actual Chess has this problem too - White has a large edge by modern game design standards! - but players have decided to just ignore it.)