For 14C dating of ice, only a limitad amount of CO2 is available (20-100 mg C/kg ice). To avoid contamination, a special miling device has been constructed to chip the ice at -20°C. The background of 7.0 +/- 2.0 percent modern carbon (pmC) for a sample of 50 mgC, including extraction and conversion, limits the 14C dating of ice with accelerator mass spectroscopy (AMS) to about 20 000 years B.P. Results are presented for an ice core from the Pakitsoq area, West Greenland, with a known age of 9000 +/- 1000 years B.P., established by means of delta-18O variations and ice flow model calculations.