Microvalves are critical in the operation of integrated microfluidic chips for a wide range of applications. In this paper, we present an analytical model to guide the design of electrostatic microvalves that can be integrated into microfluidic chips using standard fabrication processes and can reliably operate at low actuation potentials (<250 V). Based on the analytical model, we identify design guidelines and operational considerations for elastomeric electrostatic microvalves and formulate strategies to minimize their actuation potentials, while maintaining the feasibility of fabrication and integration. We specifically explore the application of the model to design microfluidic microvalves fabricated in poly(dimethylsiloxane), using only soft-lithographic techniques. We discuss the electrostatic actuation in terms of several microscale phenomena, including squeeze-film damping and adhesion-driven microvalve collapse. The actuation potentials predicted by the model are in good agreement with experimental data obtained with a microfabricated array of electrostatic microvalves actuated in air and oil. The model can also be extended to the design of peristaltic pumps for microfluidics and to the prediction of actuation potentials of microvalves in viscous liquid environments. Additionally, due to the compact ancillaries required to generate low potentials, these electrostatic microvalves can potentially be used in portable microfluidic chips.