The great majority of international contracts provides that eventual disputes should be decided by arbitration. Legal scholars argue that international arbitration is leading to the development of a legal doctrine attuned to the needs of business and independent of national laws. This paper studies international arbitration as a beautiful example of the role of private trade in shaping international institutions. We review the provisions and the practice of international arbitration, and present a general equilibrium model of the relationship between the expansion of international trade and the adoption of arbitration. The model focusses on the heterogeneity existing among economic agents in terms of their legal needs. It shows how arbitration alters the size and composition of markets, while at the same time responding to exogenous changes in trade. In addition, it shows how the legal services provided by the courts deteriorate in the presence of arbitration and predicts that the share of traders using arbitration should rise as markets expand. Overall, the model does remarkably well in generating results commonly discussed in the legal literature.