The phase fcc FeH x (x~1) was synthesized at pressures over 30GPa and temperatures over 1600(50)K. At room temperature this iron hydride is stable at pressures from 19(1)GPa up to at least 68(2)GPa (the highest pressure achieved in this study). A fit of the PV data collected for fcc FeH x at room temperature gives the following parameters for the equation of state: V 0 =53.8(3) Å 3 , K 0 =99(5) GPa, K′=11.7(5). Using this data the amount of H required to match the density of the Earth's core was estimated to be 0.5–1wt.% hydrogen in the outer core and 0.08–0.16wt.% hydrogen in the inner core. Our results also suggest that hydrogen and carbon do not occur together in the Earth's core.