We report on the discovery of Gliese 12 b, the nearest transiting temperate, Earth-sized planet found to date. Gliese 12 is a bright (V = 12.6 mag, K = 7.8 mag) metal-poor M4V star only 12.162 ± 0.005 pc away from the Solar system with one of the lowest stellar activity levels known for M-dwarfs. A planet candidate was detected by TESS based on only 3 transits in sectors 42, 43, and 57, with an ambiguity in the orbital period due to observational gaps. We performed follow-up transit observations with CHEOPS and ground-based photometry with MINERVA-Australis, SPECULOOS, and Purple Mountain Observatory, as well as further TESS observations in sector 70. We statistically validate Gliese 12 b as a planet with an orbital period of 12.76144 ± 0.00006 d and a radius of 1.0 ± 0.1 R⊕, resulting in an equilibrium temperature of ~315 K. Gliese 12 b has excellent future prospects for precise mass measurement, which may inform how planetary internal structure is affected by the stellar compositional environment. Gliese 12 b also represents one of the best targets to study whether Earth-like planets orbiting cool stars can retain their atmospheres, a crucial step to advance our understanding of habitability on Earth and across the galaxy.