Polarization switching in ferroelectrics has been thought to occur only through the nucleation and growth of new domains. Here we use in situ synchrotron x-ray scattering to monitor switching controlled by applied chemical potential. In sufficiently thin PbTiO₃ films, nucleation is suppressed and switching occurs by a continuous mechanism, i.e., by uniform decrease and inversion of the polarization without domain formation. The observed lattice parameter shows that the electric field in the film during switching reaches the theoretical intrinsic coercive field.