This paper studies how productivity asymmetry across countries affects the formation of global free trade. Our model extends the three-country endowment model of Bagwell and Staiger (1999) by introducing production and productivity heterogeneity across countries. We show that if all three countries have the same productivity, global free trade is always the only equilibrium. Then we consider two cases of productivity asymmetry: (i) one highly-productive country and two less-productive countries and (ii) two highly-productive countries and one less-productive country. The mechanism is that a highly productive country has a more elastic supply curve and recognizes that its trading partners' unilaterally optimal tariffs are relatively small under the status quo. In both cases, we show that (i) when productivity levels are sufficiently similar, the equilibrium is a global free trade; and (ii) when productivities are sufficiently asymmetric, the equilibrium outcome is that the two similarly productive countries sign a bilateral free trade agreement while the other country does not participate. We test the main model prediction using panel data from 195 countries between 1990 to 2017. We find empirical evidence that a pair of countries with similar productivity levels are more likely to sign a bilateral trade agreement.