We have investigated the phase relations in the iron-rich portion of the iron-silicon (Fe-Si) alloys at high pressures and temperatures. Our study indicates that Si alloyed with Fe can stabilize the body-centered cubic (bcc) phase up to at least 84 gigapascals (compared to approximately 10 gigapascals for pure Fe) and 2400 kelvin. Earth's inner core may be composed of hexagonal close-packed (hcp) Fe with up to 4 weight percent Si, but it is also conceivable that the inner core could be a mixture of a Si-rich bcc phase and a Si-poor hcp phase.