The Mishnah Berurah 637:1 says its forbidden to build a sukkah on yom tov or to fix the schach if it fell off. However, through a non jew יש להתיר, he says it's permissible.
Im curious what is the heter. My impression is building a sukkah is a melacha doraisa, either binyan, or at least setting up the schach should be the melacha of ohel. My understanding is the issur derabanan of asking a non jew to do melacha is alleviated when it's שבות דשבות במקום מצוה, when you're asking them to break a derabanan for the sake of a mitzvah (SA 307:5). Here if the melacha is doraisa, how can you ask them? Or does he mean hint to them (not sure if that helps)? Or here since it's the issue of not having a sukkah, there's more leeway?