  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.
