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We present Magellan/IMACS spectroscopy of the recently-discovered Milky Waysatellite Eridanus II (Eri II). We identify 28 member stars in Eri II, fromwhich we measure a systemic radial velocity of $v_{\rm hel} = 75.6 \pm1.3~\mbox{(stat.)} \pm 2.0~\mbox{(sys.)}~\mathrm{km\,s^{-1}}$ and a velocitydispersion of $6.9^{+1.2}_{-0.9}~\mathrm{km\,s^{-1}}$. Assuming that Eri~II isa dispersion-supported system in dynamical equilibrium, we derive a mass withinthe half-light radius of Eri II is $1.2^{+0.4}_{-0.3} \times10^{7}~\mathrm{M_\odot}$, indicating a mass-to-light ratio of$420^{+210}_{-140}~\mathrm{M_\odot}/\mathrm{L_\odot}$ and confirming that it isa dark matter-dominated dwarf galaxy. From the equivalent width measurements ofthe CaT lines of 16 red giant member stars, we derive a mean metallicity of${\rm [Fe/H]} = -2.38 \pm 0.13$ and a metallicity dispersion of $\sigma_{\rm[Fe/H]} = 0.47 ^{+0.12}_{-0.09}$. The velocity of Eri II in the GalacticStandard of Rest frame is $v_{\rm GSR} = -66.6~\mathrm{km\,s^{-1}}$, indicatingthat either Eri II is falling into the Milky Way potential for the first timeor it has passed the apocenter of its orbit on a subsequent passage. At aGalactocentric distance of $\sim$370 kpc, Eri II is one of the Milky Way's mostdistant satellites known. Additionally, we show that the bright blue starspreviously suggested to be a young stellar population are not associated withEri II. The lack of gas and recent star formation in Eri II is surprising givenits mass and distance from the Milky Way, and may place constraints on modelsof quenching in dwarf galaxies and on the distribution of hot gas in the MilkyWay halo. Furthermore, the large velocity dispersion of Eri II can be combinedwith the existence of a central star cluster to constrain MACHO dark matterwith mass $\gtrsim10~\mathrm{M_\odot}$.

Farthest Neighbor: The Distant Milky Way Satellite Eridanus II