  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 numerically 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 $F_P > 70$). In combination, these
parameters could enable the development of highly coherent spin-photon
interfaces, ready for integration into nanophotonic circuits.
