Because of dissolution of lighter elements such as sulfur, carbon, hydrogen, and oxygen, Earth’s outer core is about 10 percent less dense than molten iron at the relevant pressure and temperature conditions. To determine whether hydrogen can account for a major part of the density deficit and is therefore an important constituent in the molten iron outer core, the hydrogen concentration in molten iron was measured at 7.5 gigapascals. From these measurements, the metal-silicate melt partitioning coefficient of hydrogen was determined as a function of temperature. If the magma ocean of primordial Earth was hydrous, more than 95 mole percent of H2O in this ocean should have reacted with iron to form FeHx, and about 60 percent of the density deficit is reconciled by adding hydrogen to the core.