This paper develops an open economy growth model in which firm heterogeneity increases the gains from trade. Technology spillovers from incumbent firms to entrants cause the productivity threshold for firm survival to grow over time as competition becomes tougher. By raising the profits of exporters, trade increases the entry rate and generates a dynamic selection effect that leads to higher growth. The paper shows that the gains from trade can be decomposed into: static gains that equal the total gains from trade in an economy without technology spillovers, and; dynamic gains that are strictly positive. Since trade raises growth through selection, not scale effects, the positive growth effect of trade vanishes when firms are homogeneous. Thus, firm heterogeneity creates a new source of dynamic gains from trade. Calibrating the model to the U.S. economy implies that dynamic selection approximately triples the gains from trade.