The principle of the primacy of the law of the European Union (EU) establishes that, where the law of the EU conflicts with the laws of its Member States (MSs), the law of the EU takes precedence over the laws of the MSs. This article evaluates the doctrinal status of the principle of primacy in response to the press release of the Court of Justice of the European Union (European Court of Justice (ECJ)) on the judgment of Germany’s Federal Constitutional Court of 5 May 2020, which breached the principle. It argues that respect of the absolute and exclusive, final jurisdiction of the ECJ under Article 267 of the Treaty on the Functioning of the European Union (TFEU) is – to quote from the press release – ‘the only way of ensuring’ the supremacy of EU law and also the direct effect and equality of EU law.