The phase equilibria of the binary water + helium system are examined at high temperatures and pressures. The equilibrium surface in T, p, x space (where T denotes temperature p pressure, and x mole fraction) has been determined experimentally. The coordinates of the critical curve are also identified to 180 MPa. The critical curve commences from the critical point of water and proceeds directly to higher temperatures and pressures without passing through a temperature minimum. This behavior is characteristic of "gas-gas immiscibility" of the first kind. Supercritical molar volumes are also reported at temperatures of 683, 703, and 723 K and pressures from 60 to 200 MPa. The critical curve was calculated using different equations of state and compared with experimental data. Equations of state based on an accurate representation of the repulsive interaction of hard spheres (e.g., the Carnahan-Starling model) failed to adequately predict the critical locus whereas calculations using the simple van der Waals equation were quantitatively accurate. Using the van der Waals equation yields very good results for both the pressure-temperature and pressure-composition behavior of this system. It is concluded that theoretically accurate hard-sphere models overestimate the contribution of repulsive interactions between helium and water.