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Shareholder primacy is the most fundamental concept in corporate law and corporate governance. It is widely embraced in the business, legal, and academic communities. Economic analysis and policy arguments advance a normative theory that corporate managers should maximize shareholder wealth. Academic literature invariably describes shareholder primacy as a “norm.” But whether the concept is “law” is contested because, remarkably, we still do not have a coherent legal theory. Our understanding of a fundamental tenet of the field is flawed and incomplete. This article presents a positive legal theory of shareholder primacy. It answers the questions: Is shareholder primacy law? What form of law is it? How does it work? The core prescription to maximize profit is misunderstood as a social norm because it cannot be in the form of an enforceable rule, the framework of a board’s fiduciary duty. Such form of law would be internally incoherent with the structure of corporate law. However, to influence behavior the concept of law is not limited to a rule‒sanction form. Pervasive judicial acceptance of a principle can legitimate a rule and thus impose a strong internal sense of obligation. This article conducts the first empirical study of case law discussing profit maximization for the period 1900 to 2016. It shows that shareholder primacy has become a Hartian obligation and a rule of law. The rule does not exist in a single locus duty, but instead is a filamentary principle that weaves through many other rules of corporate law and the architecture of the corporate and market systems. This article shows how the obligation, albeit unenforceable, is efficacious nonetheless.