The location of a half monolayer of ordered hydrogen adatoms on Ni(111) has been analyzed by Low-Energy Electron Diffraction (LEED), Thermal Desorption Spectroscopy (TDS), and Work Function (Δφ) measurements. It is found that the hydrogen atoms are arranged in an overlayer of graphitic structure with a (2×2) unit cell with respect to the substrate unit cell. In the ordered regions, the hydrogen adatoms occupy both types of three fold hollow sites without a detectable difference in the Ni-H bond lengths between the two sites. The Ni-H bond length is found to be 1.84±0.06 Å, corresponding to an overlayer-substrate spacing of 1.15±0.1 Å. The relation between this structure and its observed order-disorder phase diagram as a function of temperature and hydrogen coverage is discussed. The disorder is discussed in detail, and a novel ''atomic band structure'' interpretation is given.