Chirality, or handedness, is a geometrical property denoting a lack of mirror symmetry. Chiral systems are ubiquitous in nature and are associated with the non-reciprocal interactions observed in topological materials and complex biomolecules, among other phenomena. In this paper, we demonstrate that chiral arrangements of dipole-coupled quantum emitters can facilitate the unidirectional transport of photonic spin excitations without breaking time-reversal symmetry. We show that this spin-selective transport stems from a universal emergent spin-orbit coupling induced by the chiral geometry, which in turn, results in a nontrivial topology. We also examine the effects of collective dissipation on the dynamics and find that many-body coherences lead to helicity-dependent photon emission: an effect we call helical superradiance. Applications to emerging quantum technologies as well as the potential role of spin-selective photon transport in nature are discussed.