We investigate the role of networks of alliances in preventing (multilateral) interstate wars. We first show that, in the absence of international trade, no network of alliances is peaceful and stable. We then show that international trade induces peaceful and stable networks: trade increases the density of alliances so that countries are less vulnerable to attack and also reduces countries' incentives to attack an ally. We present historical data on wars and trade, noting that the dramatic drop in interstate wars since 1950, and accompanying densification and stabilization of alliances, are consistent with the model but not other prominent theories.