We study the innovation effects of the Agreement on the Free Movement of Persons (AFMP), signed by Switzerland and the EU in 1999. Using geocoded patent data, complemented by matched inventor-immigrant-census records, we identify a large number of cross-border inventors (CBIs), commuters from neighbouring countries working in Swiss R&D labs. We show that, during the AFMP implementation phase, the influx of CBIs increased differentially across regions at different driving distances from the border, causing a 24% increase in patents, mostly due to large and medium patent holders (as opposed to very large ones) and to inventor teams mixing CBIs and natives. We do not detect any adverse effect on native inventors and show that Swiss incumbent inventors collaborating with CBIs increased their productivity. Our evidence suggests complementarity between CBIs' and Swiss incumbents' knowledge assets.