A new analytical technique with sufficient sensitivity to determine 81Kr concentrations in groundwater is described. The method utilizes single-atom counting by laser resonance ionization spectroscopy (RIS) in combination with a small spectrometer to achieve the required selectivity and sensitivity. A first demonstration of the technique for groundwater analyses is presented in which about 1000 atoms of 81Kr were counted after the processing of gas extracted from only a few liters of water. The potential of the new method for groundwater dating the the range 50,000 to 1,000,000 years is discussed.