Research in social sciences other than economics indicates substantial differences in behaviour between men and women. The general conclusion drawn from this work is that women will be more socially-orientated (selfless), and men more individually-orientated (selfish). This paper reports the results of a double-anonymous dictator experiment designed to permit the emergence of basic gender differences in economic behaviour. Our results are intended to provide a baseline for further research. We find that women, on average, donate twice as much as men to their anonymous partners when any factors that might confound cooperation are eliminated.