In the atmospheres of Earth and Mars, xenon is strongly depleted relative to argon, when compared to the abundances in chondritic meteorites. The origin of this depletion is poorly understood. Here we show that more than one weight per cent of argon may be dissolved in MgSiO(3) perovskite, the most abundant phase of Earth's lower mantle, whereas the xenon solubility in MgSiO(3) perovskite is orders of magnitude lower. We therefore suggest that crystallization of perovskite from a magma ocean in the very early stages of Earth's history concentrated argon in the lower mantle. After most of the primordial atmosphere had been lost, degassing of the lower mantle replenished argon and krypton, but not xenon, in the atmosphere. Our model implies that the depletion of xenon relative to argon indicates that perovskite crystallized from a magma ocean in the early history of Earth and perhaps also Mars.