  We prove a chain rule of local type for a class of fractional hypoelliptic
equations of Kolmogorov-Fokker-Planck type. We introduce a semigroup based
notion of nonlocal \emph{carr\'e du champ} which works successfully in
situations in which the infinitesimal generator of the semigroup itself does
not necessarily possess a gradient. Our results extend and sharpen the original
2004 chain rule due to A. C\'ordoba and D. C\'ordoba.
