High-resolution x-ray diffraction provides evidence that potassium (K) alloys with iron (Fe) when the two pure elements are heated together at pressures above ~26 gigapascals (GPa). Increases of 2--3% in volume of the ϵ (hexagonal close packed: hcp) high-pressure phase of Fe can be attributed to the incorporation of ~1 atomic% (~7000 ppm by weight) K into Fe. Our results provide experimental support for predictions, derived from quantum mechanical calculations, that pressure can induce the alloying of K with Fe due to a change in the chemical-bonding character of K from alkaline- to transition-metal. Radioactive decay through the incorporation of 40K into the core could therefore be an important source of energy deep inside the Earth, helping to power the geodynamo and mantle dynamics.