What is the effect of dispersed levels of cognitive ability of members of a (business) team on their team's performance? This paper reports the results of a field experiment in which 573 students in 49 teams start up and manage real companies under identical circumstances. We ensured exogenous variation in - otherwise random - team composition by assigning students to teams based on their measured cognitive abilities (Raven test). Each team performs a variety of tasks, often involving complex decision making. The key result of the experiment is that the performance of business teams first increases and then decreases with ability dispersion. We seek to understand this finding by developing a model in which team members of different ability levels form sub-teams with other team members with similar ability levels to specialize in different productive tasks. Diversity spreads production over different tasks in order to escape diminishing marginal returns under specialization. The model comes with a boundary condition: our experimental finding is most likely to emerge in settings where different tasks exhibit moderate differences in their productive contributions to total output.