The Court of Justice of the European Union (CJEU) uses a chamber system to more efficiently decide cases. To what extent, and under what conditions, does the CJEU’s chamber system undermine the consistency of the Court’s application of EU law? This paper contributes to the literature on the internal organization of collegial courts by presenting a computational formal model that predicts (a) that hearing cases in smaller chambers undermines the consistency of the Court’s application of EU law and (b) that the magnitude of this effect is larger when judges’ preferences are more heterogeneous and smaller when plaintiffs strategically bring cases. Based on these findings, I use machine learning and empirical data on CJEU judgments in infringement cases to estimate the degree to which we should expect the chamber system to undermine the consistency of the CJEU’s application of EU law in practice.