We describe a feasibility experiment to demonstrate high-order adaptive optics using a sodium-layer laser guide star. We use the copper-vapor-pumped dye lasers developed for LLNL`s atomic Vapor Laser Isotope Separation program to create the laser guide star. Closed-loop adaptive corrections will be accomplished using a 69-subaperture adaptive optics system on a one-meter telescope at LLNL. The laser bream is projected upwards from a beam director approximately 5 meters away from the main telescope, and is expected to form a spot 1-2 meters in diameter at the atmospheric sodium layer (95 km altitude). We describe the overall system architecture and adaptive optics components, and analyze the expected performance. Our long-term goal is to develop sodium-layer laser guide stars and adaptive optics for large astronomical telescopes. We discuss preliminary design trade-offs for the Keck Telescope at Mauna Kea.