The separation of krypton and xenon is of particular importance for the field of direct dark matter search with liquid xenon detectors. The intrinsic contamination of the xenon with radioactive (85)Kr makes a significant background for these kinds of low count-rate experiments and has to be removed beforehand. This can be achieved by cryogenic distillation, a technique widely used in industry, using the different vapor pressures of krypton and xenon. In this paper, we present an investigation on the separation performance of a single stage distillation system using a radioactive (83m)Kr-tracer method. The separation characteristics under different operation conditions are determined for very low concentrations of krypton in xenon at the level of (83m)Kr/Xe = 1.9 ⋅ 10(-15), demonstrating, that cryogenic distillation in this regime is working. The observed separation is in agreement with the expectation from the different volatilities of krypton and xenon. This cryogenic distillation station is the first step on the way to a multi-stage cryogenic distillation column for the next generation of direct dark matter experiment XENON1T.