The inner core, most remote part of our planet, is composed of solid iron. Because the relevant ultrahigh pressure and temperature conditions were only accessible by dynamical shock-wave compression experiments, the crystal structure of iron at the inner core has long been under debate. Our first static experiments show that the hexagonal close-packed (hcp) structure is a stable form of iron up to 377 GPa and 5700 K, 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 cause inner core seismic anisotropy.