The Jewish Festival of Lights apparently has no “correct” spelling – it is a transliteration of a Hebrew word into English. Rabbi Daniel Zemel of Washington, DC was asked by NPR about the spelling, and this is what he had to say:
“There’s several different difficult letters in terms of the transliteration,” he says. “There’s the (Hebrew spoken), there’s the (Hebrew spoken) and there’s the (Hebrew spoken), then there’s the (Hebrew spoken) at the end. And all of them have legitimately different variations on how to properly transliterate them.” (NPR.org)
The Rabbi also said he had to attend a committee at his synagogue to agree on which spelling would be put on their publicity materials – they went with C-H-A-N-U-K-K-A-H.