Cosmochemical, geochemical, and geophysical studies provide evidence that Earth's core contains iron with substantial (5 to 15%) amounts of nickel. The iron-nickel alloy Fe(0.9)Ni(0.1) has been studied in situ by means of angle-dispersive x-ray diffraction in internally heated diamond anvil cells (DACs), and its resistance has been measured as a function of pressure and temperature. At pressures above 225 gigapascals and temperatures over 3400 kelvin, Fe(0.9)Ni(0.1) adopts a body-centered cubic structure. Our experimental and theoretical results not only support the interpretation of shockwave data on pure iron as showing a solid-solid phase transition above about 200 gigapascals, but also suggest that iron alloys with geochemically reasonable compositions (that is, with substantial nickel, sulfur, or silicon content) adopt the bcc structure in Earth's inner core.