Phase separation of molecular condensates is emerging as a key mechanism in biology and biomaterials science. A major advantage of condensates is their capacity to form and reconfigure dynamically, generating responsive compartments that organize molecular targets and reactions in both space and time, in the absence of membranes. While condensation is known to depend on environmental conditions such as temperature and ionic strength, biological condensates in nature are likely influenced by fluctuating biochemical signals with high specificity. Here we ask whether the behavior of artificial condensates can be controlled via chemical reactions by design. Through theory and experiments we examine a model problem in which a phase separating component participates in chemical reactions that activate and deactivate its ability to self-attract. Our theoretical model indicates that such reactions have effects comparable to temperature, and illustrates the dependence of condensate kinetics on reaction parameters. We experimentally realize our model problem through a platform that combines DNA nanostar motifs to generate condensate droplets, and strand displacement reactions to kinetically control the nanostar valency. Our results show that DNA condensate dissolution and growth can be controlled reversibly via toehold-mediated strand displacement, and we characterize the influence of toehold and invasion domains, nanostar size, and nanostar valency. In some cases, the reduction of nanostar valency through invasion stabilizes the droplet size. Our results provide foundational methods for the development of dynamic nucleic acid condensates with potential applications in biomaterials science, nanofabrication, and drug delivery.