The European Union is the world's deepest free trade zone. Amongst its members, it has abolished tariffs and lowered non-tariff barriers. This has led to trade creation within Europe and to trade diversion between EU countries and outsiders. Deep trade integration and the resulting mutual dependence has, in the eyes of many, facilitated political integration. The Transatlantic Trade and Investment Partnership (TTIP) will undo some of these effects by means of preference erosion, so that cross-country trade links within Europe may lose relative prominence. However, the presence of a rich fabric of regional value chains in Europe and substantial income effects could counter this development. We provide insights on the empirical importance of these effects based on a New Quantitative Trade Model. We show that TTIP could indeed lower trade integration in Europe since predicted income effects turn out not to be large enough to overcome the effects of preference erosion. However, there is substantial heterogeneity across sectors and countries. One way to minimize preference erosion would be to promote projects and programs to further deepen the EU's single market.