Chiral light-matter interactions can enable polarization to control the direction of light emission in a photonic device. Most realizations of chiral light-matter interactions require external magnetic fields to break time-reversal symmetry of the emitter. One way to eliminate this requirement is to utilize strong spin-orbit coupling present in transition metal dichalcogenides that exhibit a valley-dependent polarized emission. Such interactions were previously reported using plasmonic waveguides, but these structures exhibit short propagation lengths due to loss. Chiral dielectric structures exhibit much lower loss levels and could therefore solve this problem. We demonstrate chiral light-matter interactions using spin-valley states of transition metal dichalcogenide monolayers coupled to a dielectric waveguide. We use a photonic crystal glide-plane waveguide that exhibits chiral modes with high field intensity, coupled to monolayer WSe2. We show that the circularly polarized emission of the monolayer preferentially couples to one direction of the waveguide, with a directionality as high as 0.35, limited by the polarization purity of the bare monolayer emission. This system enables on-chip directional control of light and could provide new ways to control spin and valley degrees of freedom in a scalable photonic platform. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement