Four superstructure phases are being observed in a combined low-energy electron-diffraction, thermal-desorption mass-spectroscopy, and work-function-change study of hydrogen adsorption on rhodium (311). This relatively open surface offers sites of threefold and fourfold coordination for the hydrogen atoms. Three low-coverage phases, 1 X 3-H, 1 X 2-H, and 1 X 3-2H, observed in the temperature range of 90-250 K, are governed by the lateral interaction of the adsorbate and seem to have little influence on the surface structure of the substrate. The high-coverage 1 X 2 phase, however, is an example of adsorbate-induced reconstruction. In contrast to the previous phases, each of which corresponds to a well-defined coverage THETA less-than-or-equal-to 2/3, the reconstructed phase appears close to THETA = 1 and cannot be saturated. Its well-ordered surface structure remains stable even under extended exposure to hydrogen. The reconstruction apparently opens diffusion channels to subsurface sites. Structural models based on a linear arrangement of hydrogen along the densely packed Rh rows are proposed for all four adsorption phases, taking into account the observed reaction kinetics of desorbing hydrogen.