10 speed upgrade

hi, I have a flat bar tourer that started life as a drop bar with 8 speed shimano triple chainset but over the years it has slowly been converted to 9 speed but the triple chainset is still the same (although it has had ne chainrings) I now want to put drop bars back on it but the bars and shifter I have are 10 speed ,I have detailer ,chain, and cassette all 10 speed so I can change everything .my question is will a 10 speed chain run on what was originally a 8 speed chainset.
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