The XENON1T experiment aims for the direct detection of dark matter in a detector filled with 3.3 tons of liquid xenon. In order to achieve the desired sensitivity, the background induced by radioactive decays inside the detector has to be sufficiently low. One major contributor is the β -emitter 85 Kr which is present in the xenon. For XENON1T a concentration of natural krypton in xenon natKr/Xe<200ppq (parts per quadrillion, 1 ppq =10−15mol/mol) is required. In this work, the design, construction and test of a novel cryogenic distillation column using the common McCabe–Thiele approach is described. The system demonstrated a krypton reduction factor of 6.4⋅10⁵ with thermodynamic stability at process speeds above 3 kg/h. The resulting concentration of natKr/Xe<26ppq is the lowest ever achieved, almost one order of magnitude below the requirements for XENON1T and even sufficient for future dark matter experiments using liquid xenon, such as XENONnT and DARWIN.