Atmospheric turbulence severely limits the resolution of ground-based telescopes. Adaptive optics can correct for the aberrations caused by the atmosphere, but requires a bright wavefront reference source in close angular proximity to the object being imaged. Since natural reference stars of the necessary brightness are relatively rare, methods of generating artificial reference beacons have been under active investigation for more than a decade. In this paper, we report the first significant image improvement achieved using a sodium-layer laser guide star as a wavefront reference for a high-order adaptive optics system. An artificial beacon was created by resonant scattering from atomic sodium in the mesosphere, at an altitude of 95 km. Using this laser guide star, an adaptive optics system on the 3 m Shane Telescope at Lick Observatory produced a factor of 2.4 increase in peak intensity and a factor of 2 decrease in full width at half maximum of a stellar image, compared with image motion compensation alone. The Strehl ratio when using the laser guide star as the reference was 65% of that obtained with a natural guide star, and the image full widths at half maximum were identical, 0.3 arc sec, using either the laser or the natural guide star. This sodium-layer laser guide star technique holds great promise for the world's largest telescopes.