This paper is a response to the call for models of organization design as a science revealing the inner composition of organization and specifying the laws to be respected when crafting it. It maintains that the needed science is a chemistry of organization, addressing the combination of 'organizational elements' playing a role analogous to that of chemical elements in composing a variety of substances. Drawing both on classic organization design theory and on configurational and complementarity-based approaches, the paper specifies a set of basic organizational elements and a set of combinatory laws regulating their effective combinations. Testable propositions are derived on the necessary and sufficient conditions that the composition of organizations should have respect for achieving high levels of efficiency and innovation. These propositions are tested empirically on a sample of firms, using an innovative application of Boolean algebra.