  An important background in detectors using liquid xenon for rare event
searches arises from the decays of radon and its daughters. We report for the
first time a reduction of $^{222}$Rn in the gas phase above a liquid xenon
reservoir. We show a reduction factor of $\gtrsim 4$ for the $^{222}$Rn
concentration in boil-off xenon gas compared to the radon enriched liquid
phase. A semiconductor-based $\alpha$-detector and miniaturized proportional
counters are used to detect the radon. As the radon depletion in the boil-off
gas is understood as a single-stage distillation process, this result
establishes the suitability of cryogenic distillation to separate radon from
xenon down to the $10^{-15}\,$mol/mol level.
