We report the detection of a transiting Earth-size planet around GJ 357, a nearby M2.5 V star, using data from the Transiting Exoplanet Survey Satellite (TESS). GJ 357 b (TOI-562.01) is a transiting, hot, Earth-sized planet (Teq = 525 ± 11 K) with a radius of Rb = 1.217 ± 0.084 R☉ and an orbital period of Pb = 3.93 d. Precise stellar radial velocities from CARMENES and PFS, as well as archival data from HIRES, UVES, and HARPS also display a 3.93-day periodicity, confirming the planetary nature and leading to a planetary mass of Mb = 1.84 ± 0.31 M☉. In addition to the radial velocity signal for GJ 357 b, more periodicities are present in the data indicating the presence of two further planets in the system: GJ 357 c, with a minimum mass of Mc = 3.40 ± 0.46 M☉ in a 9.12 d orbit, and GJ 357 d, with a minimum mass of Md = 6.1 ± 1.0 M☉ in a 55.7 d orbit inside the habitable zone. The host is relatively inactive and exhibits a photometric rotation period of Prot = 78 ± 2 d. GJ 357 b is to date the second closest transiting planet to the Sun, making it a prime target for further investigations such as transmission spectroscopy. Therefore, GJ 357 b represents one of the best terrestrial planets suitable for atmospheric characterization with the upcoming JWST and ground-based ELTs.