Entangled-photon pairs are an essential resource for quantum-information technologies. Chip-scale sources of entangled pairs have been integrated with various photonic platforms, including silicon, nitrides, indium phosphide, and lithium niobate, but each has fundamental limitations that restrict the photon-pair brightness and quality, including weak optical nonlinearity or high waveguide loss. Here, we demonstrate a novel ultralow-loss AlGaAs-on-insulator platform capable of generating time-energy entangled photons in a Q > 1 million microring resonator with nearly 1000-fold improvement in brightness compared to existing sources. The waveguide-integrated source exhibits an internal generation rate greater than 20 x 10(9) pairs s(-1) mW(-2), emits near 1550 nm, produces heralded single photons with > 99% purity, and violates Bell's inequality by more than 40 standard deviations with visibility > 97%. Combined with the high optical nonlinearity and optical gain of AlGaAs for active component integration, these are all essential features for a scalable quantum photonic platform.