  We present the characterization of the star KOI 961, an M dwarf with transit
signals indicative of three short-period exoplanets, originally discovered by
the Kepler Mission. We proceed by comparing KOI 961 to Barnard's Star, a
nearby, well-characterized mid-M dwarf. By comparing colors, optical and
near-infrared spectra, we find remarkable agreement between the two, implying
similar effective temperatures and metallicities. Both are metal-poor compared
to the Solar neighborhood, have low projected rotational velocity, high
absolute radial velocity, large proper motion and no quiescent H-alpha
emission--all of which is consistent with being old M dwarfs. We combine
empirical measurements of Barnard's Star and expectations from evolutionary
isochrones to estimate KOI 961's mass (0.13 +/- 0.05 Msun), radius (0.17 +/-
0.04 Rsun) and luminosity (2.40 x 10^(-3.0 +/- 0.3) Lsun). We calculate KOI
961's distance (38.7 +/- 6.3 pc) and space motions, which, like Barnard's Star,
are consistent with a high scale-height population in the Milky Way. We perform
an independent multi-transit fit to the public Kepler light curve and
significantly revise the transit parameters for the three planets. We calculate
the false-positive probability for each planet-candidate, and find a less than
1% chance that any one of the transiting signals is due to a background or
hierarchical eclipsing binary, validating the planetary nature of the transits.
The best-fitting radii for all three planets are less than 1 Rearth, with KOI
961.03 being Mars-sized (Rp = 0.57 +/- 0.18 Rearth), and they represent some of
the smallest exoplanets detected to date.
