Ab initio quantum mechanical calculations show that xenon (Xe) can be alloyed with hexagonal close-packed iron at high pressure through substitutional incorporation, with a favorable enthalpy of formation for the alloy relative to the separate elemental solids, suggesting that Xe is soluble in the Earth's iron-rich core (up to ~0.8 mol %). This alloying behavior and the possible presence of a significant amount of Xe in the core are important for understanding the accretion and evolution of the Earth and its atmosphere.