One of the key issues in the relationship between EU law and national law is the question of which body – the Court of Justice of the European Union or the constitutional courts of the Member States – acts as the ultimate arbiter of the scope of EU competences. This issue has been reflected in two divergent answers: on the one hand, that of the CJEU, and on the other, that of certain constitutional courts of the Member States. In this context, particular attention should be given to the proposal to establish a Joint Chamber of Highest Courts and Tribunals of the EU, designed to resolve competence disputes of significant constitutional importance arising between the EU and a Member State. The purpose of this paper is to analyse this proposal, and in particular to assess whether it could provide a solution to the dispute over the “final say” in the EU constitutional order.