Measurements of Kr-84/Ar-36 ratios in Greenland ice show that gravitational separation in the firn layer is responsible for the enrichments relative to atmospheric ratios. The Kr-84/Ar-36 ratio is enriched by 12.8 per mil and is 24 times the O-18/O-16 enrichment in trapped O-2, as predicted for gravitational fractionation. Because gravitational enrichment depends on firn thickness, which in turn depends on annual mean temperature, noble gas ratios provide a method for determining paleotemperatures and ancient firn thicknesses in polar ice caps, The gravitational effects are modulated by about 10 to 15 percent by atmospheric concentration changes caused by temperature effects on oceanic gas solubilities. The availability of five noble gases should make it possible to deconvolute the solubility and gravitational enrichments for calibration of O-18 paleotemperatures throughout the polar ice sheets.