How does trade policy affect competition? Using the universe of product exports by firms from eleven low and middle-income countries, we document that tariff reductions under trade agreements have strong pro-competitive effects - they encourage entry and reduce the (tariff exclusive) price-cost markups of exporters. This finding, that markups fall with tariff cuts, contradicts a core prediction of standard oligopolistic competition models of trade. We extend a workhorse international pricing model of oligopolistic competition to include multiple countries and a rich preference structure. Our preference structure allows for fierce competition among firms from the same country and less intense competition among firms from different countries. We show a firm's optimal markup after a tariff cut can rise or fall depending on the parameters of the preference structure and tari-induced reallocation of market share among firms and across countries.