  We present low-resolution spectroscopy of 120 red giants in the Galactic
satellite dwarf spheroidal (dSph) Leo I, obtained with the GeminiN-GMOS and
Keck-DEIMOS spectrographs. We find stars with velocities consistent with
membership of Leo I out to 1.3 King tidal radii. By measuring accurate radial
velocities with a median measurement error of 4.6 km/s we find a mean systemic
velocity of 284.2 km/s with a global velocity dispersion of 9.9 km/s. The
dispersion profile is consistent with being flat out to the last data point. We
show that a marginally-significant rise in the radial dispersion profile at a
radius of 3' is not associated with any real localized kinematical
substructure. Given its large distance from the Galaxy, tides are not likely to
have affected the velocity dispersion, a statement we support from a
quantitative kinematical analysis, as we observationally reject the occurrence
of a significant apparent rotational signal or an asymmetric velocity
distribution. Mass determinations adopting both isotropic stellar velocity
dispersions and more general models yield a M/L ratio of 24, which is
consistent with the presence of a significant dark halo with a mass of about
3x10^7 M_sun, in which the luminous component is embedded. This suggests that
Leo I exhibits dark matter properties similar to those of other dSphs in the
Local Group. Our data allowed us also to determine metallicities for 58 of the
targets. We find a mildly metal poor mean of -1.31 dex and a full spread
covering 1 dex. In contrast to the majority of dSphs, Leo I appears to show no
radial gradient in its metallicities, which points to a negligible role of
external influences in this galaxy's evolution.
