A simulation scheme for performing first-principles molecular dynamics at a constant electrode potential is presented, opening the way for a more realistic modeling of voltage-driven devices. The system is allowed to exchange electrons with a reservoir at fixed potential, and dynamical equations for the total electronic charge are derived by using the potential energy of the extended system. In combination with a thermostat, this potentiostat scheme reproduces thermal fluctuations of the charge with the correct statistics, implying a realistic treatment of the potential as a control variable. Practically, the dynamics of the charge are decoupled from the electronic structure calculations, making the scheme easily implementable in existing first-principles molecular dynamics codes. Our approach is demonstrated on a test system by considering various test cases.