  We present Magellan/M2FS, VLT/GIRAFFE, and Gemini South/GMOS spectroscopy of
the newly discovered Milky Way satellite Reticulum II. Based on the spectra of
25 Ret II member stars selected from Dark Energy Survey imaging, we measure a
mean heliocentric velocity of 62.8 +/- 0.5 km/s and a velocity dispersion of
3.3 +/- 0.7 km/s. The mass-to-light ratio of Ret II within its half-light
radius is 470 +/- 210 Msun/Lsun, demonstrating that it is a strongly dark
matter-dominated system. Despite its spatial proximity to the Magellanic
Clouds, the radial velocity of Ret II differs from that of the LMC and SMC by
199 and 83 km/s, respectively, suggesting that it is not gravitationally bound
to the Magellanic system. The likely member stars of Ret II span 1.3 dex in
metallicity, with a dispersion of 0.28 +/- 0.09 dex, and we identify several
extremely metal-poor stars with [Fe/H] < -3. In combination with its
luminosity, size, and ellipticity, these results confirm that Ret II is an
ultra-faint dwarf galaxy. With a mean metallicity of [Fe/H] = -2.65 +/- 0.07,
Ret II matches Segue~1 as the most metal-poor galaxy known. Although Ret II is
the third-closest dwarf galaxy to the Milky Way, the line-of-sight integral of
the dark matter density squared is log J = 18.8 +/- 0.6 Gev^2/cm^5 within 0.2
degrees, indicating that the predicted gamma-ray flux from dark matter
annihilation in Ret II is lower than that of several other dwarf galaxies.
