We present Magellan/IMACS spectroscopy of the recently-discovered Milky Way satellite Eridanus II ( Eri II ) . We identify 28 member stars in Eri II , from which we measure a systemic radial velocity of v _ { hel } = 75.6 \pm 1.3 ~ { } \mbox { ( stat . ) } \pm 2.0 ~ { } \mbox { ( sys . ) } \mathrm { km } \mathrm { s } ^ { -1 } and a velocity dispersion of 6.9 ^ { +1.2 } _ { -0.9 } \mathrm { km } \mathrm { s } ^ { -1 } . Assuming that Eri II is a dispersion-supported system in dynamical equilibrium , we derive a mass within the half-light radius of 1.2 ^ { +0.4 } _ { -0.3 } \times 10 ^ { 7 } \mathrm { M _ { \odot } } , indicating a mass-to-light ratio of 420 ^ { +210 } _ { -140 } \mathrm { M _ { \odot } } / \mathrm { L _ { \odot } } and confirming that it is a dark matter-dominated dwarf galaxy . From the equivalent width measurements of the CaT lines of 16 red giant member stars , we derive a mean metallicity of \mbox { [ Fe / H ] } = -2.38 \pm 0.13 and a metallicity dispersion of \sigma _ { \mbox { [ Fe / H ] } } = 0.47 ^ { +0.12 } _ { -0.09 } . The velocity of Eri II in the Galactic Standard of Rest frame is v _ { GSR } = -66.6 \mathrm { km } \mathrm { s } ^ { -1 } , indicating that either Eri II is falling into the Milky Way potential for the first time or it has passed the apocenter of its orbit on a subsequent passage . At a Galactocentric distance of \sim 370 kpc , Eri II is one of the Milky Way ’ s most distant satellites known . Additionally , we show that the bright blue stars previously suggested to be a young stellar population are not associated with Eri II . The lack of gas and recent star formation in Eri II is surprising given its mass and distance from the Milky Way , and may place constraints on models of quenching in dwarf galaxies and on the distribution of hot gas in the Milky Way halo . Furthermore , the large velocity dispersion of Eri II can be combined with the existence of a central star cluster to constrain MACHO dark matter with mass \gtrsim 10 \mathrm { M _ { \odot } } .