It isn't one included in The Letters of JRRTolkien edited by Humphrey Carpenter with the assistance of Christopher Tolkien, but that volume doesn't contain all his letters. The signature looks like it was Tolkien's compared to that at the front of the book. The handwriting is different, but he said he was in a hurry and apologized for the illegibility, so that isn't conclusive. I'd assume it is real until proven otherwise, but I certainly wouldn't spend any money towards buying it without certified documentation.
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