  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 $12.162\pm0.005$ pc away from the Solar System
with one of the lowest stellar activity levels known for an M-dwarf. 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 $12.76144\pm0.00006$ days and
a radius of $1.0\pm{0.1}$ R$_\oplus$, resulting in an equilibrium temperature
of $\sim$315K. 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.
