We analyze Ukraine's opportunities to participate in European value chains, using traditional gravity models, combined with tools from Economic Complexity Analysis to study international trade (exports) and Foreign Direct Investment (FDI). This toolbox is shown to be predictive of the growth and entry of new exports to the EU's Single Market, as well as foreign direct investments from the Single Market in Ukraine. We find that Ukraine has suffered from a decline of trade with Russia, which has led not only to a quantitative but also a qualitative deterioration in Ukrainian exports. Connecting to western European value chains is in principle possible, with several opportunities in the automotive, information technology and other sectors. However, such a shift may lead to a spatial restructuring of the Ukrainian economy and a mismatch between the geographical supply of and demand for labor.