Knowledge of the outgassing history of radiogenic (40)Ar, derived over geologic time from the radioactive decay of (40)K, contributes to our understanding of the geodynamic history of the planet and the origin of volatiles on Earth's surface. The (40)Ar inventory of the atmosphere equals total (40)Ar outgassing during Earth history. Here, we report the current rate of (40)Ar outgassing, accessed by measuring the Ar isotope composition of trapped gases in samples of the Vostok and Dome C deep ice cores dating back to almost 800 ka. The modern outgassing rate (1.1 +/- 0.1 x 10(8) mol/yr) is in the range of values expected by summing outgassing from the continental crust and the upper mantle, as estimated from simple calculations and models. The measured outgassing rate is also of interest because it allows dating of air trapped in ancient ice core samples of unknown age, although uncertainties are large (+/-180 kyr for a single sample or +/-11% of the calculated age, whichever is greater).