Dissipative (nonequilibrium) assembly powered by chemical fuels has great potential for the creation of new adaptive chemical systems. However, while molecular assembly at equilibrium is routinely used to prepare complex architectures from polyfunctional monomers, species formed out of equilibrium have, to this point, been structurally very simple. In most examples the fuel simply effects the formation of a single transient covalent bond. Here, we show that chemical fuels can assemble bifunctional components into macrocycles containing multiple transient bonds. Specifically, dicarboxylic acids give aqueous dianhydride macrocycles on treatment with a carbodiimide. The macrocycle is assembled efficiently as a consequence of both fuel-dependent and -independent mechanisms: it undergoes slower decomposition, building up as the fuel recycles the components, and is a favored product of the dynamic exchange of the anhydride bonds. These results create new possibilities for generating structurally sophisticated out-of-equilibrium species.