A new method of permafrost dating with the cosmogenic radionuclide 36Cl is presented. In the first application, syngenetic ice wedges are dated using the ratio of 36Cl and Cl concentrations in ice as the signal. 36Cl is produced in the atmosphere by nuclear reactions of cosmic rays on argon. Stable chlorine enters the atmosphere from the oceans. The isotopes transfer in atmosphere together, and their ratio does not depend on chloride concentration in precipitations and on sublimation of snow. In situ production of 36Cl in permafrost ice via cosmic ray-induced reactions and neutron capture are calculated and the dating age limit is estimated as 2 million years. 36Cl/Cl ratios in the mid and late Pleistocene syngenetic ice wedges of Cape Svyatoy Nos and Bol'shoy Lyakhovsky Island, are measured by accelerator mass spectrometry. Analysis of the first results and the calculated dates support the feasibility of the 36Cl permafrost dating method.