Male and female choices differ in many economic situations, e.g., on the labor market. This paper considers whether such differences are driven by different attitudes towards competition. In our experiment subjects choose between a tournament and a piece-rate pay scheme before performing a real task. Men choose the tournament significantly more often than women. Women are mainly influenced by their degree of risk aversion, but men are not. Men compete more against men than against women, but compete against women who are thought to compete. The behavior of men seems primarily to be influenced by social norms whose nature and origin we discuss.