Atom trap trace analysis, a laser-based atom counting method, has been applied to analyze atmospheric 39Ar (half-life=269 yr), a cosmogenic isotope with an isotopic abundance of 8×10(-16). In addition to the superior selectivity demonstrated in this work, the counting rate and efficiency of atom trap trace analysis have been improved by 2 orders of magnitude over prior results. The significant applications of this new analytical capability lie in radioisotope dating of ice and water samples and in the development of dark matter detectors.