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We report the discovery of a transiting, temperate, Neptune-sized exoplanet orbiting the nearby ($d$ = 27.5 pc), M3V star TOI-1231 (NLTT 24399, L 248-27, 2MASS J10265947-5228099). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite and followed up with observations from the Las Cumbres Observatory and the Antarctica Search for Transiting ExoPlanets program. Combining the photometric data sets, we find that the newly discovered planet has a radius of 3.65$^{+0.16}_{-0.15}$ R$_{\oplus}$, and an orbital period of 24.246 days. Radial velocity measurements obtained with the Planet Finder Spectrograph on the Magellan Clay telescope confirm the existence of the planet and lead to a mass measurement of 15.5$\pm$3.3 M$_{\oplus}$. With an equilibrium temperature of just 330K TOI-1231 b is one of the coolest small planets accessible for atmospheric studies thus far, and its host star's bright NIR brightness (J=8.88, K$_{s}$=8.07) make it an exciting target for HST and JWST. Future atmospheric observations would enable the first comparative planetology efforts in the 250-350 K temperature regime via comparisons with K2-18 b. Furthermore, TOI-1231's high systemic radial velocity (70.5 k\ms) may allow for the detection of low-velocity hydrogen atoms escaping the planet by Doppler shifting the H I Ly-alpha stellar emission away from the geocoronal and ISM absorption features.