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We have obtained radial velocities of 31 red giants in the Leo II dSph galaxy using the HIRES echelle spectrograph of the Keck 10m telescope. The systemic velocity of Leo II is 76.0 $\pm$ 1.3 km/s, and the velocity dispersion is 6.7 $\pm$ 1.1 km/s. The global V band mass-to-light ratio (M/L) -- calculated assuming that mass follows light and an isotropic velocity distribution -- is 11.1 $\pm$ 3.8, with a central value of 11.6 $\pm$ 3.2, in solar units. This M/L is larger than that seen in any star clusters. For a constant density system, a model independent lowest-possible central mass density is 0.074 solar masses per parsec cubed, which is larger than the luminous mass density for M/L=2. Because Leo~II's light profile does not correspond to a constant-density system if M/L = constant, this result implies very large M/L values in the outer part of Leo~II. We conclude that Leo~II contains dark matter. The M/L of Leo~II is that expected for its absolute magnitude, based on measurements of other dwarf galaxies. In particular, the dark halo has a mass of $0.9 \times 10^7 M_\odot$, similar to the masses of dark halos in all other dSph systems that have been adequately observed. This work was supported by NSF grants to EO, and MM.
