In this paper I quantify the welfare gains of the 2004 EU enlargement as a result of the abolition of border controls, both for incumbents and for new members. I build a multi-sector Ricardian model, allowing for linkages across sectors, similar to the one in Caliendro and Parro (2011). As with a large number of quantitative trade models, the gains crucially depend on one key parameter, the dispersion of productivity. I extend the estimation methodology of Costinot et al. (2012) to a richer modeling setting and compute the dispersion in a way consistent with the underlying theoretical model. Within the model, I compare the welfare changes for 23 countries between 2003 and 2006. I find that new entrants gained significantly more than old members from enlargement. However, the overall changes in real income are rather small, measured in single digits for new entrants and fractions of a percent for old members. I also break down total gains by source and find that allowing for interconnectedness across sectors amplifies the changes in welfare.