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Mmm yeah it's spelt "cheek". It's an excellent suggestion but I don't think it quite gets at the essence of chutzpah (nothing does, which is probably the point).
Cheek is a brilliant British word, but it can't be used for anything that's genuinely important. Whereas I think that chutzpah can.
Translation rightly depends on circumstances, but with no other context, I'd go for "effrontery" as the best English option for chutzpah.