In this study, we have investigated, using the atom superposition and electron delocalization (ASED) band technique, the structures and energetics for the sequential addition of hydrogen atoms to the extended {1010BAR} zigzag edge of a graphite sheet. The calculations show that H can chemisorb strongly on the unsaturated rings located on the edge of the graphite sheet, transforming them to their fully saturated analogues. Cluster model calculations show that hydrogen atoms can adsorb to a graphite sheet far from the edge, causing a distortion toward the tetrahedral structure for the carbon atoms to which they are bound, but the CH bond strengths are significantly less than at the edge. In our first edge model, hydrogen addition commences at the outermost zigzag carbon chain and proceeds into the sheet by progressively distorting an increasing number of planar rings to the all-chair saturated ring configuration. In this case, H atoms are added successively and alternately on the top and bottom of various carbon rows along the zigzag edge. In our second model, the H atoms are added to only one face of the sheet, resulting in the formation of saturated rings in the all-boat configuration. This causes the edge of the sheet to curl over on itself, and H addition beyond the third zigzag carbon chain leads to strong steric interactions which will limit this mode of hydrogenation and may cause fragmentation. At high temperatures, H insertion will compete with H addition, which will be responsible for the formation of a variety of products including various saturated ring systems as observed by Rye. In a low-pressure diamond growth environment, diamond nucleation is likely to commence on the hydrogenated graphite edges.