Spin-dependent, directional light-matter interactions form the basis of chiral quantum networks. In the solid state, quantum emitters commonly possess circularly polarised optical transitions with spin-dependent handedness. We demonstrate theoretically that spin-dependent chiral coupling can be realised by embedding such an emitter in a waveguide-coupled nanocavity, which supports two near-degenerate, orthogonally-polarised cavity modes. The chiral behaviour arises due to direction-dependent interference between the cavity modes upon coupling to two single-mode output waveguides. Notably, an experimentally realistic cavity design simultaneously supports near-unity chiral contrast, efficient ($beta > 0.95$) waveguide coupling and enhanced light-matter interaction strength (Purcell factor $F_P > 60$). In combination, these parameters could enable the development of highly coherent spin-photon interfaces, and may even allow access to the chiral strong-coupling regime using integrated nano-photonic devices.
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