We present a spectroscopic study of Leo V, a recently discovered satellite of the Milky Way (MW). From stellar spectra obtained with the MMT/Hectochelle spectrograph we identify seven likely members of Leo V. Five cluster near the Leo V center (R < 3') and have a velocity dispersion of 2.4+2.4 –1.4 km s–1. The other two likely members lie near each other but far from the center (R ~ 13' ~ 700 pc) and inflate the global velocity dispersion to 3.7+2.3 –1.4 km s–1. Assuming the five central members are bound, we obtain a dynamical mass of M = 3.3+9.1 –2.5 × 105 M ☉ (M/LV = 75+230 –58[M/LV ]☉). From the stacked spectrum of the five central members we estimate a mean metallicity of [Fe/H]=–2.0 ± 0.2 dex. Thus, with respect to dwarf spheroidals of similar luminosity, Leo V is slightly less massive and slightly more metal rich. Since we resolve the central velocity dispersion only marginally, we do not rule out the possibility that Leo V is a diffuse star cluster devoid of dark matter. The wide separation of its two outer members implies Leo V is losing mass; however, its large distance (D ~ 180 kpc) is difficult to reconcile with MW tidal stripping unless the orbit is very radial.