A new method for dating polar ice or other environmental Samples which are 50,000 years to 1,000,000 years old is proposed, based on the direct measurements of cosmogenic 81Kr (half-life = 210,000 yrs.). The method consists of isotopic enrichment of the krypton extracted from the ice followed by ultrasensitive detection of the 81Kr using the laser-based technique of Resonance Ionization Spectroscopy. Feasibility of the 81Kr technique will be demonstrated by measuring 81Kr in two old ice samples and two modern ice samples collected from the Allan Hills area of Antarctica. The results will provide the basis for development of a commercial 81Kr-dating facility which will have important applications, in addition to polar ice dating, in groundwater dating, hydrology, solar neutrino studies, and meteorite studies.