We report the local-conductivity properties of a La0.8Ca0.2MnO3 thin film, studied by conductive atomic force microscopy. Nonvolatile and bipolar reversible switching of nanometer-sized regions was observed. A threshold voltage, U-c approximate to 3 V, and a logarithmic pulse-width dependence compatible with domain-wall creep were revealed. The results are difficult to explain in terms of an ionic drift scenario but rather indicate a switching mechanism based on orbital and accompanying structural changes. A phenomenological model of an electric field-induced structural transition is proposed.