+1, a 9s chain works fine for 8s or 7s. It's slightly narrower than necessary, but it won't be an issue.
Just about the only way it could (rarely) become a problem is if you have fairly wide chainring spacing, and the narrower chain hangs between the tips of the inner ring's teeth and the face of the outer. But this is far more common when using a 10s chain for 9s, than a 9s for 8s since most cranksets have the same chainring separation for 8s and 9s.
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