Generating and interfering non-classical states of light is fundamental to optical quantum information science and technology. Quantum photonic integrated circuits provide one pathway towards scalability by combining nonlinear sources of non-classical light and programmable circuits in centimeter-scale devices. The key requirements for quantum applications include efficient generation of indistinguishable photon-pairs and high-visibility programmable quantum interference. Here, we demonstrate a lithium niobate-on-insulator (LNOI) integrated photonic circuit that generates a two-photon path-entangled state, and a programmable interferometer for quantum interference. We generate entangled photons with $\sim2.3\times10^8$ pairs/s/mW brightness and perform quantum interference experiments on the chip with $96.8\pm3.6\%$ visibility. LNOI is an emerging photonics technology that has revolutionized high-speed modulators and efficient frequency conversion. Our results provide a path towards large-scale integrated quantum photonics including efficient photon-pair generation and programmable circuits for applications such as boson sampling and quantum communications.