  Spin-orbit coupled dynamics are of fundamental interest in both quantum
optical and condensed matter systems alike. In this work, we show that photonic
excitations in pseudospin-1/2 atomic lattices exhibit an emergent spin-orbit
coupling when the geometry is chiral. This spin-orbit coupling arises naturally
from the electric dipole interaction between the lattice sites and leads to
spin polarized excitation transport. Using a general quantum optical model, we
determine analytically the conditions that give rise to spin-orbit coupling and
characterize the behavior under various symmetry transformations. We show that
chirality-induced spin textures are associated with a topologically nontrivial
Zak phase that characterizes the chiral setup. Our results demonstrate that
chiral atom arrays are a robust platform for realizing spin-orbit coupled
topological states of matter.
