In the wake of the U.S.-Canada Free Trade Agreement, both the U.S. and Canada experienced a sustained increase in job reallocation, including firms moving into exporting. The change was concentrated in industries with steeper tariff cuts, and involved big firms as much as small firms. To mimic these patterns, we formulate a model of innovation by both domestic and foreign firms. In the model, trade liberalization quickens the pace of creative destruction, thereby speeding the flow of technology across countries. The resulting dynamic gains from trade liberalization are an order of magnitude larger than the gains in a standard static model.