Materials with strong $chi^{(2)}$ optical nonlinearity, especially lithium niobate, play a critical role in building optical parametric oscillators (OPOs). However, chip-scale integration of low-loss $chi^{(2)}$ materials remains challenging and limits the threshold power of on-chip $chi^{(2)}$ OPO. Here we report the first on-chip lithium niobate optical parametric oscillator at the telecom wavelengths using a quasi-phase matched, high-quality microring resonator, whose threshold power ($sim$30 $mu$W) is 400 times lower than that in previous $chi^{(2)}$ integrated photonics platforms. An on-chip power conversion efficiency of 11% is obtained at a pump power of 93 $mu$W. The OPO wavelength tuning is achieved by varying the pump frequency and chip temperature. With the lowest power threshold among all on-chip OPOs demonstrated so far, as well as advantages including high conversion efficiency, flexibility in quasi-phase matching and device scalability, the thin-film lithium niobate OPO opens new opportunities for chip-based tunable classical and quantum light sources and provides an potential platform for realizing photonic neural networks.