To identify literary influences is, conventionally, to build a genealogy—to, in Salman Rushdie’s words, “name one’s parents.” But can this family-tree view of literary influence hold up in postcolonial literature—a body of work that has so thoroughly deconstructed concepts of genealogy? This article turns to a pivotal case of “influence” in postcolonial Francophone literature and philosophy: among Édouard Glissant and Gilles Deleuze and Félix Guattari. The latter two writers are thought to have influenced Glissant’s thinking with their concept of the “rhizome,” but the rhizome directly counters such genealogizing as this “influence” would imply. In fact, this article shows, Glissant develops his own version of the rhizome from his very earliest writings, particularly his first poems. An analysis of them alongside Glissant’s subsequent essays and Deleuze and Guattari’s own writing, allows for a more complicated, multidirectional—that is, rhizomatic—theory of postcolonial influence.