The exercise of leadership by the chairs of multilateral negotiations has so far received limited systematic attention in scholarship on international cooperation. This article addresses this gap by presenting a rational institutionalist theory of formal leadership that provides answers to three central questions: Why do states delegate powers of process control to the chairmanship of international negotiations? What are the power resources of formal leaders? And when, why and how do negotiation chairs wield influence over the outcomes of multilateral bargaining? The theory suggests that chairmanships are empowered to fulfil functions of agenda management, brokerage, and representation in international bargaining; identifies procedural control and privileged information as essential power resources of negotiation chairs; and isolates the conditions under which formal leaders shape the efficiency and distributional implications of multilateral bargaining. The article ends by outlining an alternative theoretical approach to formal leadership, drawn from sociological institutionalism.