At low pressures, the solubility of gases in liquids is governed by Henry's law, which states that the saturated solubility of a gas in a liquid is proportional to the partial pressure of the gas. As the pressure increases, most gases depart from this ideal behavior in a sublinear fashion, leveling off at pressures in the 1- to 5-kbar (0.1 to 0.5 GPa) range with solubilities of less than 1 mole percent (mol %). This contrasts strikingly with the well-known marked increase in solubility of simple gases in water at high temperature associated with the critical point (647 K and 212 bar). The solubility of the smallest hydrocarbon, the simple gas methane, in water under a range of pressure and temperature is of widespread importance, because it is a paradigmatic hydrophobe and occurs widely in terrestrial and extraterrestrial geology. We report measurements up to 3.5 GPa of the pressure dependence of the solubility of methane in water at 100°C-well below the latter's critical temperature. Our results reveal a marked increase in solubility between 1 and 2 GPa, leading to a state above 2 GPa where the maximum solubility of methane in water exceeds 35 mol %.