We highlight a coordination problem between the EU Emissions Trading System (ETS) and the EU's offshore renewable energy strategy. We exemplify this coordination failure by analyzing carbon leakage effects associated with Denmark's planned North Sea energy island. The Danish energy island project will not start production before 2033, implying a long interval between project announcement and production. Using a dynamic model of the EU ETS, we show that the large time gap between announcement and production likely results in a ‘Green Paradox’, where the energy island increases aggregate EU ETS emissions. The mechanism leading to the emission increase is complicated and works through the Market Stability Reserve (MSR). The estimated 2050 leakage rate is 145 percent in our main scenario and not below 100 percent in any alternative scenario. We discuss how to improve the climate benefits of the energy island or similar large-scale renewable energy projects. This includes possible revisions to the EU ETS and the role of Power-to-X technologies.