Earth's solid inner core is mainly composed of iron (Fe). Because the relevant ultrahigh pressure and temperature conditions are difficult to produce experimentally, the preferred crystal structure of Fe at the inner core remains uncertain. Static compression experiments showed that the hexagonal close-packed (hcp) structure of Fe is stable up to 377 gigapascals and 5700 kelvin, corresponding to inner core conditions. The observed weak temperature dependence of the c/a axial ratio suggests that hcp Fe is elastically anisotropic at core temperatures. Preferred orientation of the hcp phase may explain previously observed inner core seismic anisotropy.