We show a causal impact of immigration on innovation and dynamism in US counties. To identify the causal impact of immigration, we use 130 years of detailed data on migrations from foreign countries to US counties to isolate quasi-random variation in the ancestry composition of US counties that results purely from the interaction of two historical forces: (i) changes over time in the relative attractiveness of different destinations within the US to the average migrant arriving at the time and (ii) the staggered timing of the arrival of migrants from different origin countries. We then use this plausibly exogenous variation in ancestry composition to predict the total number of migrants flowing into each US county in recent decades. We show four main results. First, immigration has a positive impact on innovation, measured by the patenting of local firms. Second, immigration has a positive impact on measures of local economic dynamism. Third, the positive impact of immigration on innovation percolates over space, but spatial spillovers quickly die out with distance. Fourth, the impact of immigration on innovation is stronger for more educated migrants.