  The combination of high-contrast imaging and high-dispersion spectroscopy,
which has successfully been used 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$_2$.
