Given that the Paris Agreement has strengthened the long-term temperature goal and that it calls for a balance of greenhouse gas (GHG) emissions and sinks within the 21st century, there is the urgent need to re-assess the long-term targets of the EU and to show how the target of GHG neutrality can be reached in the EU. The aim of this study was to design one way to realize a European Union with net-zero greenhouse gas emissions under further sustainability criteria. The scenario shows that a GHG-neutral EU is feasible, based on a fully decarbonized energy supply, without carbon capture and storage. Key components of the scenario in all energy-consuming sectors are a strong increase in energy efficiency as well as far-reaching electrification. The use of bioenergy is strongly limited.