We demonstrate a high-purity source of indistinguishable single photons using a quantum dot embedded in a nanophotonic waveguide. The source features a near-unity internal coupling efficiency and the collected photons are efficiently coupled off-chip by implementing a taper that adiabatically couples the photons to an optical fiber. By quasi-resonant excitation of the quantum dot, we measure a single-photon purity larger than 99.4% and a two-photon interference visibility of 62+-2%, which is a measure of the degree of indistinguishability of subsequently emitted photons. A temperature-dependent study of photon indistinguishability allows pinpointing the residual decoherence processes as due to excitation-induced photon jitter and phonon decoherence. The study opens a clear pathway towards a fully deterministic source of indistinguishable photons integrated on a planar photonic chip.