Spin–orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. In the optical domain, an analogous synthetic spin–orbit coupling is accessible by engineering optical anisotropies in photonic materials. Both yield the possibility of creating devices that directly harness spin and polarization as information carriers. Atomically thin transition metal dichalcogenides promise intrinsic spin-valley Hall features for free carriers, excitons and photons. Here we demonstrate spin- and valley-selective propagation of exciton-polaritons in a monolayer of MoSe₂ that is strongly coupled to a microcavity photon mode. In a wire-like device we trace the flow and helicity of exciton-polaritons expanding along its channel. By exciting a coherent superposition of K and K′ tagged polaritons, we observe valley-selective expansion of the polariton cloud without either an external magnetic field or coherent Rayleigh scattering. The observed optical valley Hall effect occurs on a macroscopic scale, offering the potential for applications in spin-valley-locked photonic devices.