Many U.S. businessmen are vocally in favor of an increase in the number of H-1B visas. Is there systematic evidence that this would positively affect firms' productivity, sales, employment or profits? To address these questions we assemble a unique dataset that matches all labor condition applications (LCAs) – the first step towards H-1B visas for skilled foreign-born workers in the U.S. – with firm-level data on publicly traded U.S. firms (from Compustat). Our identification is based on the sharp reduction in the annual H-1B cap that took place in 2004, combined with information on the degree of dependency on H-1B visas at the firm level as in Kerr and Lincoln (2010). The main result of this paper is that if the cap on H-1B visas were relaxed, a subset of firms would experience gains in average labor productivity, firm size, and profits. These are firms that conduct R&D and are heavy users of H-1B workers – they belong to the top quintile among filers of LCAs. These empirical findings are consistent with a heterogeneous-firms model where innovation enhances productivity and is subject to fixed costs.