Recent experiments suggest that the high hydrogen storage capacity in graphite nanostructures might be associated with adsorption on the edges. First-principles calculations are used to study the structure and energetics of H chemisorption on graphite zigzag edges. The properties of both singly and doubly hydrogenated edges are examined. Molecular hydrogen can dissociatively adsorb on the edge directly, with small activation barriers to the formation of either singly or doubly hydrogenated structures. A new model for the location of adsorbed H is proposed.