In this paper we show that the pluripolar hull of$E$={($z$, ω)∈C^{2}:ω=$e$^{−1/z},$z$≠0} is equal to$E$. This implies that$E$is plurithin at 0, which answers a question of Sadullaev. The result remains valid if$e$^{−1/z}is replaced by certain other holomorphic functions with an essential singularity at 0.