Segue 2, discovered by Belokurov et al. (2009, Cat. J/MNRAS/397/1748), is a galaxy with a luminosity of only 900L_{sun}_. We present Keck/DEIMOS spectroscopy of 25 members of Segue 2 - a threefold increase in spectroscopic sample size. The velocity dispersion is too small to be measured with our data. The upper limit with 90% (95%) confidence is {sigma}_v_<2.2(2.6)km/s, the most stringent limit for any galaxy. The corresponding limit on the mass within the three-dimensional half-light radius (46pc) is M_1/2_<1.5(2.1)x10^5^M_{sun}_. Segue 2 is the least massive galaxy known. We identify Segue 2 as a galaxy rather than a star cluster based on the wide dispersion in [Fe/H] (from -2.85 to -1.33) among the member stars. The stars' [{alpha}/Fe] ratios decline with increasing [Fe/H], indicating that Segue 2 retained Type Ia supernova ejecta despite its presently small mass and that star formation lasted for at least 100 Myr. The mean metallicity, <[Fe/H]>=-2.22+/-0.13 (about the same as the Ursa Minor galaxy, 330 times more luminous than Segue 2), is higher than expected from the luminosity-metallicity relation defined by more luminous dwarf galaxy satellites of the Milky Way. Segue 2 may be the barest remnant of a tidally stripped, Ursa Minor-sized galaxy. If so, it is the best example of an ultra-faint dwarf galaxy that came to be ultra-faint through tidal stripping. Alternatively, Segue 2 could have been born in a very low mass dark matter subhalo (v_max_<10km/s), below the atomic hydrogen cooling limit.