We compare winning and losing firms in lotteries for H-1B visas, matching administrative data on these lotteries to administrative tax data on U.S. firms and to approved U.S. patents. Winning one additional H-1B visa crowds out about 1.5 other workers at the firm. Additional H-1Bs have insignificant and at most modest effects on firm innovation. More general evidence from the universe of U.S. firms and the universe of H-1B visas using alternative estimation strategies is consistent with these results. Firms that hire H-1Bs grow faster and innovate more because they are different in other ways from firms that do not.