The Milky Way galaxy contains a large, spherical component which is believed to harbor a substantial amount of unseen matter. Recent observations indirectly suggest that as much as half of this ``dark matter'' may be in the form of old, very cool white dwarfs, the remnants of an ancient population of stars as old as the galaxy itself. We conducted a survey to find faint, cool white dwarfs with large space velocities, indicative of their membership in the galaxy's spherical halo component. The survey reveals a substantial, directly observed population of old white dwarfs, too faint to be seen in previous surveys. This newly discovered population accounts for at least 2 percent of the halo dark matter. It provides a natural explanation for the indirect observations, and represents a direct detection of galactic halo dark matter.