We have observed 19 giant stars in the Draco dwarf spheroidal (dSph) galaxy and obtained good quality spectra for 17 of these. The velocity dispersion of the sample, calculated by the maximum-likelihood method, is 10.5+/-^2.2_1.7 km s^-1. The mean velocity is -293.8+/-^2.6_2.7 km s^-1. The data were taken at a single epoch, so there is no direct information about possible binary star contamination. Assuming dynamical equilibrium, isotropy in the velocity dispersion and a negligible contribution from binary stars, the core mass-to-light ratio is 166+/-^289_107 M_/L_ and the total mass-to-light ratio is 145+/-^116_71 M_/L_, consistent with the presence of large quantities of dark matter.