This paper shows how a brain drain - the emigration of agents with a relatively high level of human capital in an economy - can paradoxically increase the productivity of an economy where productivity is a function of the average level of human capital. The model uses Galor and Tsiddon's model of income distribution, endogenous human capital formation and growth, to analyze the interaction between income distribution and migration. The paradoxical positive effect of a brain drain on productivity occurs when successful emigration is not a certainty and when the increase in human capital accumulation by people wishing to become eligible to emigrate, causes a change in the long run income distribution which outweighs the decrease in human capital caused by the brain drain itself