Quantum photon sources of high rate, brightness, and purity are increasingly desirable as quantum information systems are quickly scaled up and applied to many fields. Using a periodically poled lithium niobate microresonator on chip, we demonstrate photon-pair generation at high rates of 8.5 and 36.3 MHz using only 3.4 and 13.4 μW pump power, respectively, marking orders of magnitude improvement over the state of the art, across all material platforms. These results constitute the first direct measurement of the device's giant single photon nonlinearity. The measured coincidence to accidental ratio is well above 100 at those high rates and reaches 14682±4427 at a lower pump power. The same chip enables heralded single-photon generation at tens of megahertz rates, each with low autocorrelation g_{H}^{(2)}(0)=0.008 and 0.097 for the microwatt pumps, which marks a new milestone. Such distinct performance, facilitated by the chip device's noiseless and giant optical nonlinearity, will contribute to the forthcoming pervasive adoption of quantum optical information technologies.