Does immigration accelerate sectoral change towards high-productivity sectors? This paper uses the mass displacement of ethnic Germans from Eastern Europe to West Germany after World War II as a natural experiment to study this question. A simple two-sector model of the economy, in which moving costs prevent the marginal product of labor to be equalized across sectors, predicts that immigration boosts output per worker by expanding the high-productivity sector, but decreases output per worker within a sector. Using German district-level data from before and after the war, we find strong empirical support for these predictions.