Exporting firms face foreign exchange risk when the export contract is invoiced in a foreign currency. For instance, for firms located outside of the United States, the US dollar is often used as a vehicle currency. The cost of hedging against this risk represents an additional trade cost for exporters, which is specific to the targeted destination. In this paper, we exploit an episode of heightened tensions in the USD/EUR foreign exchange market in July 2011, which increased the cost of hedging against US dollar fluctuations for French exporters. Using disaggregated information on bank balance sheets, bank-firm relationships and individual export flows for France, we show that exporters with a higher propensity to use hedging instruments reduced more their exports to "US dollar destinations" after this shock. For the average "treated" individual export flow in our sample, the increased hedging cost is equivalent to a counterfactual rise in trade costs by about 3 percentage points.