The combination of high-contrast imaging and high-dispersion spectroscopy , which has successfully been use to detect the atmosphere of a giant planet , is one of the most promising potential probes of the atmosphere of Earth-size worlds . The forthcoming generation of extremely large telescopes ( ELTs ) may obtain sufficient contrast with this technique to detect O _ { 2 } in the atmosphere of those worlds that orbit low-mass M dwarfs . This is strong motivation to carry out a census of planets around cool stars for which habitable zones can be resolved by ELTs , i.e . for M dwarfs within \sim 5 parsecs . Our HARPS survey has been a major contributor to that sample of nearby planets . Here we report on our radial velocity observations of Ross 128 ( Proxima Virginis , GJ447 , HIP 57548 ) , an M4 dwarf just 3.4 parsec away from our Sun . This source hosts an exo-Earth with a projected mass m \sin i = 1.35 M _ { \oplus } and an orbital period of 9.9 days . Ross 128 b receives \sim 1.38 times as much flux as Earth from the Sun and its equilibrium ranges in temperature between 269 K for an Earth-like albedo and 213 K for a Venus-like albedo . Recent studies place it close to the inner edge of the conventional habitable zone . An 80-day long light curve from K2 campaign C01 demonstrates that Ross 128 b does not transit . Together with the All Sky Automated Survey ( ASAS ) photometry and spectroscopic activity indices , the K2 photometry shows that Ross 128 rotates slowly and has weak magnetic activity . In a habitability context , this makes survival of its atmosphere against erosion more likely . Ross 128 b is the second closest known exo-Earth , after Proxima Centauri b ( 1.3 parsec ) , and the closest temperate planet known around a quiet star . The 15 mas planet-star angular separation at maximum elongation will be resolved by ELTs ( > 3 \lambda / D ) in the optical bands of O _ { 2 } .