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.