We measure the extent to which skilled immigrants increase innovation in the United States by exploring individual patenting behavior as well as state-level determinants of patenting. The 2003 National Survey of College Graduates shows that immigrants patent at double the native rate, and that this is entirely accounted for by their disproportionately holding degrees in science and engineering. These data imply that a one percentage point rise in the share of immigrant college graduates in the population increases patents per capita by 6%. This could be an overestimate of immigration's benefit if immigrant inventors crowd out native inventors, or an underestimate if immigrants have positive spill-overs on inventors. Using a 1940-2000 state panel, we show that immigrants do have positive spill-overs, resulting in an increase in patents per capita of 9-18% in response to a one percentage point increase in immigrant college graduates. We isolate the causal effect by instrumenting the change in the share of skilled immigrants in a state with the state's predicted increase in the share of skilled immigrants. We base the latter on the 1940 distribution across states of immigrants from various source regions and the subsequent national increase in skilled immigrants from these regions.