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+/-11K) with a radius of R_b_=1.217+/-0.084R_{Earth} and an orbital period of P_b=3.93d. 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 existence of the planet and leading to a planetary mass of M_b_=1.84+/-0.31M_{Earth}. In addition to the radial velocity signal for GJ 357 b, more periodicities are present in the data indicating the presence of two more planets in the system: GJ 357 c, with a minimum mass of M_c=3.40+/-0.46M_{Earth} in a 9.12d orbit, and GJ 357 d, with a minimum mass of M_d=6.1+/-1.0M_{Earth}_ in a 55.7d orbit inside the habitable zone. The host is relatively inactive and exhibits a photometric rotation period of Prot=78+/-2d. 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.