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 quasiresonant excitation of the quantum dot, we measure a single-photon purity larger than 99.4% and a photon indistinguishability of up to 94±1% by using p-shell excitation combined with spectral filtering to reduce photon jitter. A temperature-dependent study allows pinpointing the residual decoherence processes, notably the effect of phonon broadening. Strict resonant excitation is implemented as well as another means of suppressing photon jitter, and the additional complexity of suppressing the excitation laser source is addressed. The paper opens a clear pathway towards the long-standing goal of a fully deterministic source of indistinguishable photons, which is integrated on a planar photonic chip.