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This paper estimates the impact of market access liberalization in high-income countries on sub-Saharan African exports. The methodology exploits the large reduction in trade barriers that was induced by three unilateral trade liberalization initiatives: (1) the dismantling of the Multi-Fiber Arrangement, (2) the African Growth and Opportunity Act in the United States, and (3) the extension of EU trade preferences for developed countries through its Everything-but-Arms program and the General System of Preferences. Using detailed product-level information at the 6-digit level of the Harmonized System and a triple-difference empirical specification, the usual endogeneity-of-policy critique is flexibly controlled for. The results indicate strongly positive export effects, which are especially large for textile, apparel, and leather products, and tend to be realized fully within 5 years. Each percentage point reduction in import tariffs raises exports to the EU by 0.73 percent and to the United States by 0.30 percent; effects are two to three times as large for textiles. The presence of strong Chinese imports has ambiguous effects on countries' ability to take advantage of trade liberalization as the impact on the export effects to the EU and the United States show an opposite sign.