We present the discovery of TOI540b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASSJ05051443-4756154. The planet has an orbital period of P=1.239149 days({+/-}170ms) and a radius of r=0.903{+/-}0.052R{Earth}, and is likely terrestrial based on the observed mass- radius distribution of small exoplanets at similar insolations. The star is 14.008pc away and we estimate its mass and radius to be M=0.159{+/-}0.014M{sun} and R=0.1895{+/-}0.0079R{sun}, respectively. The star is distinctive in its very short rotational period of Prot=17.4264{+/-}0.0094hr and correspondingly small Rossby number of 0.007 as well as its high X-ray-to-bolometric luminosity ratio of L_X_/L_bol_=0.0028 based on a serendipitous XMM-Newton detection during a slew operation. This is consistent with the X-ray emission being observed at a maximum value of L_X_/L_bol_~10^-3^ as predicted for the most rapidly rotating M dwarfs. TOI540b may be an alluring target to study atmospheric erosion due to the strong stellar X-ray emission. It is also among the most accessible targets for transmission and emission spectroscopy and eclipse photometry with the James Webb Space Telescope, and may permit Doppler tomography with high-resolution spectroscopy during transit. This discovery is based on precise photometric data from the Transiting Exoplanet Survey Satellite and ground-based follow-up observations by the MEarth team.