Does a unilateral climate change policy cause companies to shift the location of production, thereby creating carbon leakage? In this paper, we analyze the effect of the European Union Emissions Trading System (EU ETS) on the geographic distribution of carbon emissions by multinational companies. The empirical evidence is based on unique data for the period 2007-2014 from the Carbon Disclosure Project, which tracks the emissions of multinational businesses by geographic region within each company. Because they already operate from multiple locations, multinational firms should be the most prone to carbon leakage. Our data includes the regional emissions of 1,122 companies, of which 261 are subject to EU ETS regulation. We find no evidence that the EU ETS has led to a displacement of carbon emissions from Europe toward the rest of the world, including to countries with lax climate policies and within energy-intensive companies. A large number of robustness checks confirm this finding. Overall, the paper suggests that modest differences in carbon prices between countries do not induce carbon leakage.