Quantum-photonic chips,which integrate quantum light sources alongside active and passive optical elements,as well as singlephoton detectors,show great potential for photonic quantum information processing and quantum technology.Mature semiconductor nanofabrication processes allow for scaling such photonic integrated circuits to on-chip networks of increasing complexity.Second-order nonlinear materials are the method of choice for generating photonic quantum states in the overwhelming majority of linear optic experiments using bulk components,but integration with waveguide circuitry on a nanophotonic chip proved to be challenging.Here,we demonstrate such an on-chip parametric down-conversion source of photon pairs based on second-order nonlinearity in an aluminum-nitride microring resonator.We show the potential of our source for quantum information processing by measuring the high visibility anti-bunching of heralded single photons with nearly ideal state purity.Our down-conversion source yields measured coincidence rates of 80 Hz,which implies MHz generation rates of correlated photon pairs.Low noise performance is demonstrated by measuring high coincidence-to-accidental ratios.The generated photon pairs are spectrally far separated from the pump field,providing great potential for realizing sufficient on-chip filtering and monolithic integration of quantum light sources,waveguide circuits and single-photon detectors.