This paper is the first part of an enquiry taking an initial, provisional step toward the construction of a theoretical matrix called speculative jurisprudence. Toward that end, it recruits the thought of Louis Althusser, whose work has taken on new significance thanks in part to the availability of many formerly unpublished texts, the contemporary critical scrutiny of numerous commentators, and the independent emergence of several philosophical currents sharing some of his work’s key concerns. The paper offers a unique characterization of (...) Althusser’s aleatory materialism as at once a novel expression of Althusser’s ‘jurisprudential problematic’, a problematic that I argue shapes his thought as a whole, and as a means of posing the core problem of dialectical materialism. The engagement with Althusser that I propose thus intervenes in current debates about aleatory materialism, but this is subsidiary with respect to the elaboration of speculative jurisprudence as a distinct approach in philosophy and law. That mode of thought begins to acquire a degree of reality by taking Althusser’s theoretical anti-humanism as a point of departure for the articulation of a non-humanist conception of legality, in a broad sense that conjoins the territories of both traditional philosophy and legal theory. The paper concludes with a reference to the open questions that Part Two, which will appear in Althusser and Law, will take up. (shrink)