  We report the discovery of the transiting planet GJ 238 b, with a radius of
$0.566\pm0.014$ R$_{\oplus}$ ($1.064\pm0.026$ times the radius of Mars) and an
orbital period of 1.74 day. The transit signal was detected by the TESS mission
and designated TOI-486.01. The star's position close to the Southern ecliptic
pole allows for almost continuous observations by TESS when it is observing the
Southern sky. The host star is an M2.5 dwarf with $V=11.57\pm0.02$ mag,
$K=7.030\pm0.023$ mag, a distance of $15.2156\pm0.0030$ pc, a mass of
$0.4193_{-0.0098}^{+0.0095}$ M$_{\odot}$, a radius of
$0.4314_{-0.0071}^{+0.0075}$ R$_{\odot}$, and an effective temperature of
$3{,}485\pm140$ K. We validate the planet candidate by ruling out or rendering
highly unlikely each of the false positive scenarios, based on archival data
and ground-based follow-up observations. Validation was facilitated by the host
star's small size and high proper motion, of $892.633\pm0.025$ mas yr$^{-1}$.
