We reconcile international trade theory with findings of enormous plant-level heterogeneity in exporting and productivity. Our model extends basic Ricardian theory to accommodate many countries, geographic barriers, and imperfect competition. Fitting the model to bilateral trade among the United States and its 46 major trade partners, we see how well it can explain basic facts about U.S. plants: (i) productivity dispersion, (ii) the productivity advantage of exporters, (iii) the small fraction who export, (iv) the small fraction of revenues from exporting among those that do, and (v) the much larger size of exporters. We pick up all these basic qualitative features, and go quite far in matching them quantitatively. We examine counterfactuals to assess the impact of various global shifts on productivity, plant entry and exit, and labor turnover in U.S. manufacturing.