The ability to engineer photon emission and photon scattering is at the heart of modern photonics applications ranging from light harvesting, through novel compact light sources, to quantuminformation processing based on single photons. Nanophotonic waveguides are particularly well suited for such applications since they confine photon propagation to a 1D geometry thereby increasing the interaction between light and matter. Adding chiral functionalities to nanophotonic waveguides lead to new opportunities enabling integrated and robust quantum-photonic devices or the observation of novel topological photonic states. In a regular waveguide, a quantum emitter radiates photons in either of two directions, and photon emission and absorption are reverse processes. This symmetry is violated in nanophotonic structures where a non-transversal local electric field implies that both photon emission [1,2] and scattering [3] may become directional. Here we experimentally demonstrate that the internal state of a quantum emitter determines the chirality of single-photon emission in a specially engineered photonic-crystal waveguide. Single-photon emission into the waveguide with a directionality of more than 90% is observed under conditions where practically all emitted photons are coupled to the waveguide. Such deterministic and highly directional photon emission enables on-chip optical diodes, circulators operating at the single-photon level, and deterministic quantum gates. Based on our experimental demonstration, we propose an experimentally achievable and fully scalable deterministic photon-photon CNOT gate, which so far has been missing in photonic quantum-information processing where most gates are probabilistic [4]. Chiral photonic circuits will enable dissipative preparation of entangled states of multiple emitters [5], may lead to novel topological photon states [6,7], or can be applied in a classical regime to obtain highly directional photon scattering [8][9][10].Truly 1D photon-emitter interfaces are desirable for a range of applications in photonic quantum-information processing [11]. To this end, photonic-crystal waveguides constitute an ideal platform featuring on-chip integration with the ability to engineer the light-matter coupling. Recent experiments have achieved a coupling efficiency for a single quantum dot (QD) to a photoniccrystal waveguide in excess of 98%, thus constituting a deterministic 1D photon-emitter interface [12]. Standard photonic-crystal waveguides are mirror symmetric around the center of the waveguide and as a consequence the mode polarization is predominantly linear at the positions where light intensity is high. By designing a photonic-crystal waveguide that breaks this symmetry, modes that are circularly polarized at the field maxima can be engineered. We refer to this novel type of waveguide as a glide-plane waveguide (GPW), cf. Supplementary Material for further descriptions of the structural parameters. In a GPW, a QD with a circularly polarized transition dipole emits preferential...