International audienceA novel online distillation technique was developed for the XENON1T dark matter experiment to reduce intrinsic background components more volatile than xenon, such as krypton or argon, while the detector was operating. The method is based on a continuous purification of the gaseous volume of the detector system using the XENON1T cryogenic distillation column. A krypton-in-xenon concentration of (360 ± 60) ppq was achieved. It is the lowest concentration measured in the fiducial volume of an operating dark matter detector to date. A model was developed and fitted to the data to describe the krypton evolution in the liquid and gas volumes of the detector system for several operation modes over the time span of 550 days, ...