We study the impact of changing relative market access in an enlarged EU on the economies of incumbent Objective 1 regions. First, we track the impact of external opening on internal spatial configurations in a three-region economic geography model. External opening gives rise to potentially offsetting economic forces, but for most parameter configurations it is found to raise the locational attractiveness of the region that is close to the external market. Then, we explore the relation between market access and economic activity empirically, using data for European regions, and we simulate the impact of EU enlargement on Objective 1 regions. Our predicted market-access induced gains in regional GDP and manufacturing employment are up to seven times larger in regions proximate to the new accession countries than in "interior" EU regions. We also find that a future Balkans enlargement could be particularly effective in reducing economic inequalities among the EU periphery, due to the positive impact on relative market access of Greek regions.