By coupling a $Lambda$-type quantum emitter to a chiral waveguide, in which the polarization of a photon is locked to its propagation direction, we propose a controllable photon-emitter interface for quantum networks. We show that this chiral system enables the SWAP gate and a hybrid-entangling gate between the emitter and a flying single photon. It also allows deterministic storage and retrieval of single-photon states with high fidelities and efficiencies. In short, this chirally coupled emitter-photon interface can be a critical building block toward a large-scale quantum network.