Chlorinated organic compounds are important contributors to the anthropogenic enhancement of stratospheric ozone depletion. We report measurements of stratospheric isotope fractionation in such a compound. Stratospheric and tropospheric difluorodichloromethane (CF2Cl2) were found to have the largest relative 37Cl/35Cl isotope ratio difference ever measured for a natural compound. The increase of the relative isotope ratio difference with altitude was tightly correlated to the corresponding decrease in the CF2Cl2 mixing ratio. The observed relationship has a high potential to provide new insights into atmospheric chemistry and transport processes.