Over the past few years, single-photon generation has been realized in numerous systems: single molecules(1), quantum dots(2-4), diamond colour centres5 and others(6). The generation and detection of single photons play a central role in the experimental foundation of quantum mechanics(7) and measurement theory(8). An efficient and high-quality single-photon source is needed to implement quantum key distribution, quantum repeaters and photonic quantum information processing(9). Here we report the identification and formation of ultrabright, room-temperature, photostable single-photon sources in a device-friendly material, silicon carbide (SiC). The source is composed of an intrinsic defect, known as the carbon antisite-vacancy pair, created by carefully optimized electron irradiation and annealing of ultrapure SiC. An extreme brightness (2 x 10(6) counts s(-1)) resulting from polarization rules and a high quantum efficiency is obtained in the bulk without resorting to the use of a cavity or plasmonic structure. This may benefit future integrated quantum photonic devices(9).