This paper investigates the fit between strategy and structure for a decentralized global firm that may organize along product and geography dimensions. Organization serves two purposes. First, it provides for the management of spillovers across product lines and across geographies. Second, it structures the incentives of local managers as they compete against other firms. WIth respect to management, a matrix is the optimal organization for the management of conflicting spillovers, and either a product or a geography organization is optimal when spillovers are complementary. A matrix organization thus does not fit a globalization strategy based on the two principal dirvers of globalization, economies of scale and scope, since those spillovers are complementary. When spillovers are conflicting, however, and a matrix organization is optimal, the decentralized firm achieves the optimal performance of a centralized, Stackelberg leader. The theory is compared with the organization of two global firms, ABB and Unilever.