We develop a model of international trade with heterogeneous firms and endogenous quality choices. Producing higher quality involves returns to scale, it is intensive in skilled labor and high-quality inputs. Firms' quality choices are interrelated because firms sell their goods to consumers and to other firms. We estimate the model using data on manufacturing plants in Colombia before the trade liberalization, simulate a counterfactual liberalization and compare the results to post-liberalization data. Like other unilateral trade liberalizations in developing countries, the skill premium and skill intensity in manufacturing increased, and the size of firms decreased in Colombia. In the model, lower tariffs lead importers and exporters to upgrade quality, increasing the domestic demand and supply of high-quality inputs. Other firms then upgrade their own product quality, thereby amplifying these effects of domestic inputs. Relative demand for skilled labor increases in a wide range of firms, despite a contraction in sales.