We study the solubility of sodium chloride in steam and supercritical water at temperatures from 450°C to 550°C and pressures from 100 bar to 300 bar as predicted by the simple point charge water model and a simple model of the ions. We calculated the chemical potential of the sodium chloride dimer in supercritical water using a Kirkwood coupling parameter integration in which we computed via molecular simulation the reversable work required to increase the NaCl -water interactions from some reduced value to their full strength. The contribution to the chemical potential of the NaCl particle with reduced interactions we computed using the Widom test particle method. Such a two stage approach is efficient because the strong interactions between NaCl and water makes the Widom insertions of the NaCl inefficient, and a singularity at the point where the NaCl-water interactions become zero makes Kirkwood integrations to the point where the particle vanishes less accurate. We then used the quasiharmonic approximation to predict the chemical potential of the solid salt at the desired temperature and pressure. We find the predicted solubilities agree well with the available experimental measurements.