  We measure the first stellar velocity dispersion of the Leo A dwarf galaxy,
\sigma = 9.3 +- 1.3 km/s. We derive the velocity dispersion from the radial
velocities of ten young B supergiants and two HII regions in the central region
of Leo A. We estimate a projected mass of 8 +- 2.7 x10^7 solar masses within a
radius of 2 arcmin, and a mass to light ratio of at least 20 +- 6 M_sun/L_sun.
These results imply Leo A is at least ~80% dark matter by mass.
