["Review of International Economics, EarlyView. ", "\nABSTRACT\nThis paper extends the Heckscher–Ohlin–Samuelson framework to allow for heterogeneous firms with capacity constraints. We show that the central theorems of the HOS model (as well as their standard generalizations via duality) carry over to our setting. Each firm has a supply curve that arises from random draws of cost/productivity for each unit of capacity. Units of capacity with costs below a threshold are active, and this threshold is called the selection cutoff. The lower this cost cutoff, the higher the firm's productivity. We show that selection is driven by the capital intensity in entry costs relative to unit production costs in the sector. Such selection is assumed away in previous work, which consequently predicts that trade makes selection in the comparative advantage sector stricter and, hence, productivity in this sector higher. Our model shows that things are less simple and depend on the trade's effect on selection, as well as on the change in factor prices. Finally, we present empirical evidence supporting our predictions about the effect of trade on productivity using Chinese firm‐level data, when the U.S. granted permanent normal trade relations (PNTR) to China upon its WTO membership.\n"]