The chapter considers, on the one hand, the ways in which international arbitration was a source of inspiration for Philip Jessup when he elaborated the notion of transnational law. On the other hand, it considers how the notion of transnational law constitutes a relevant tool for the analysis of international arbitration. The chapter relies in particular on the documents gathered in the Philip C. Jessup Collection at the Library of Congress, which include early drafts and preparatory works for the Storrs Lectures at Yale University. It examines three discrete stories that each illustrate one salient aspect of the notion of transnational law (norms, actors and processes) and its relevance for the analysis of international arbitration.