I build a simple dynamic model of the formation of an international social network of importers and exporters. Firms can only export into markets in which they have a contact. They acquire new contacts both at random, and via their network of existing contacts. This model can explain (i) the cross-sectional distribution of the number of foreign markets accessed by individual exporters, (ii) the cross-sectional geographic distribution of foreign contacts, and (iii) the dynamics of firm level exports. All theoretical predictions have a very tight connection with the data on both firm level and aggregate trade flows.