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We report the discovery from K2 of a transiting terrestrial planet in anultra-short-period orbit around an M3-dwarf. K2-137 b completes an orbit inonly 4.3 hours, the second-shortest orbital period of any known planet, just 4minutes longer than that of KOI 1843.03, which also orbits an M-dwarf. Using acombination of archival images, AO imaging, RV measurements, and light curvemodelling, we show that no plausible eclipsing binary scenario can explain theK2 light curve, and thus confirm the planetary nature of the system. Theplanet, whose radius we determine to be 0.89 +/- 0.09 Earth radii, and whichmust have a iron mass fraction greater than 0.45, orbits a star of mass 0.463+/- 0.052 Msol and radius 0.442 +/- 0.044 Rsol.

K2-137 b: an Earth-sized planet in a 4.3-hour orbit around an M-dwarf