Using first-principles molecular dynamics (MD) simulations, we study the solubility of argon in molten iron at high pressures and temperatures. In particular we explore whether the low pressure immiscibility of liquid Fe and Ar persists to high pressure (130 GPa) and temperature (4500K), or whether they mix. Starting from a variety of Fe/Ar mixtures we find that they always separate rapidly into two liquids. We conclude that there is no evidence for a significant increase in the solubility of Ar in Fe at these conditions. We cannot, therefore, attribute the lower melting temperatures of Fe obtained from DAC experiments compared to those obtained from ab initio calculations and shock experiments, to eutectic melting between Fe and the Ar pressure medium.