We present low-resolution spectroscopy of 120 red giants in the Galactic satellite dwarf spheroidal (dSph) Leo I, obtained with GeminiN GMOS and Keck DEIMOS. 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-1, we find a mean systemic velocity of 284.2 km s-1 with a global velocity dispersion of 9.9 km s-1. 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 an M/L of 24, which is consistent with the presence of a significant dark halo with a mass of about 3 × 107 M☉, 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.