How simple chemical reactions self-assembled into complex, robust networks at the origin of life is unknown. This general problem-self-assembly of dissipative molecular networks-is also important in understanding the growth of complexity from simplicity in molecular and biomolecular systems. Here, we describe how heterogeneity in the composition of a small network of oscillatory organic reactions can sustain (rather than stop) these oscillations, when homogeneity in their composition does not. Specifically, multiple reactants in an amide-forming network sustain oscillation when the environment (here, the space velocity) changes, while homogeneous networks-those with fewer reactants-do not. Remarkably, a mixture of two reactants of different structure-neither of which produces oscillations individually-oscillates when combined. These results demonstrate that molecular heterogeneity present in mixtures of reactants can promote rather than suppress complex behaviors.