Spectroscopy of transiting exoplanets can be used to investigate their atmospheric properties and habitability. Combining radial velocity (RV) and transit data provides additional information on exoplanet physical properties. We detect a transiting rocky planet with an orbital period of 1.467 days around the nearby red dwarf star Gliese 486. The planet Gliese 486 b is 2.81 Earth masses and 1.31 Earth radii, with uncertainties of 5%, as determined from RV data and photometric light curves. The host star is at a distance of similar to 8.1 parsecs, has a J-band magnitude of similar to 7.2, and is observable from both hemispheres of Earth. On the basis of these properties and the planet's short orbital period and high equilibrium temperature, we show that this terrestrial planet is suitable for emission and transit spectroscopy.