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The seeds of all Horse-chestnuts including California Buckeye (Aesculus californica) are toxic to vertebrates if eaten,
but there would not be any significant, allelopathic effect from a germinating buckeye seed on an already established tree.
Besides the timing is wrong. The maple was ailing since last Summer and The buckeye sprouted last week.
It is true that if your Japanese Maple (Acer palmatum) is ailing in its container (rootbound? root rot?, who knows?), any other large plant competing for root space will probably hasten its demise. If you want to troubleshoot what might be wrong with the maple, describe its growing conditions and post a pic.
California Buckeye is a beautiful native tree, and better adapted to our Mediterranean climate than Japanese Maple anyway. If you want to save both trees, carefully transplant the Buckeye seedling to its own container, or in the ground ...or, if the maple really is on its way out, just leave the buckeye where it is.
Fun Fact: Both Buckeyes (Aesculus) and Maples (Acer) were formerly each in their own small families, Hippcastanaceae and Aceraceae, respectively, but modern phylogenetics has since shown it fit to include them both as members of the Soapberry family (Sapindaceae).