We measure the first stellar velocity dispersion of the Leo A dwarf galaxy , \sigma = 9.3 \pm 1.3 km s ^ { -1 } . We derive the velocity dispersion from the radial velocities of ten young B supergiants and two H ii regions in the central region of Leo A . We estimate a projected mass of 8 \pm 2.7 \times 10 ^ { 7 } ~ { } M _ { \sun } within a radius of 2 \arcmin , and a mass to light ratio of at least 20 \pm 6 ~ { } M _ { \sun } / L _ { \sun } . These results imply Leo A is at least \sim 80 % dark matter by mass .