  We present the projected velocity dispersion profile for the remote
(d=233kpc) Galactic dwarf spheroidal (dSph) galaxy Leo II, based on 171
discrete stellar radial velocities that were obtained from medium-resolution
spectroscopy using the FLAMES/GIRAFFE spectrograph at the European Southern
Observatory, Chile. The dispersion profile of those stars with good membership
probabilities is essentially flat with an amplitude of 6.6+-0.7 km/s over the
full radial extent of our data, which probe to the stellar boundary of this
galaxy. We find no evidence of any significant apparent rotation or velocity
asymmetry which suggests that tidal effects cannot be invoked to explain Leo
II's properties. From basic mass modeling, employing Jeans' equation, we derive
a mass out to the limiting radius of (2.7+-0.5) 10^7 Msun and a global mass to
light ratio of 27-45 in solar units, depending on the adopted total luminosity.
A cored halo profile and a mild amount of tangential velocity anisotropy is
found to account well for Leo II's observed kinematics, although we cannot
exclude the possibility of a cusped halo with radially varying velocity
anisotropy. All in all, this galaxy exhibits dark matter properties which
appear to be concordant with the other dSph satellites of the Milky Way, namely
a halo mass profile which is consistent with a central core and a total mass
which is similar to the common mass scale seen in other dSphs.
