We report strongly non-reciprocal behaviour for quantum dot exciton spins coupled to nano-photonic waveguides under resonant laser excitation. A clear dependence of the transmission spectrum on the propagation direction is found for a chirally-coupled quantum dot, with spin up and spin down exciton spins coupling to the left and right propagation directions respectively. The reflection signal shows an opposite trend to the transmission, which a numerical model indicates is due to direction-selective saturation of the quantum dot. The chiral spin-photon interface we demonstrate breaks reciprocity of the system and opens the way to spin-based quantum optical components such as optical diodes and circulators in a chip-based solid-state environment.