We use data on international chess tournaments to study the relationship between age and mental productivity in a brain-intensive profession. We show that less talented players tend to leave the game in the earliest phases of their career. When the effects of age on productivity vary with unobserved ability, commonly used fixed effects estimators applied to raw data do not guarantee consistent estimates of age-productivity profiles. In our data, this method strongly over-estimates the productivity of older players. We apply fixed effects to first-differenced data and show that productivity peaks in the early forties and smoothly declines thereafter. Because of this, players aged 60 are 11 percent less productive than players in their early forties.