You’re correct that a definite answer must exist, because chess is a deterministic game. But the answer is not known.
It is generally believed that a perfect game of chess ends in a draw, since the best chess computers usually draw against one another, and highly skilled human players usually draw as well. But so far, chess is not a [(weakly) solved game](https://en.wikipedia.org/wiki/Solved_game), so we don’t know for sure what the outcome of optimal play is.
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