Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.