We report a novel dc field-driven propagative instability associated with the thermally induced layer undulations of the smectic C phase in a phenyl benzoate. While the undulations are two-dimensional, the drift is observed only along the wave vector q parallel to the c director; undulations with orthogonal q and c remain stable. The drift, which is nonhysteretic, takes place in a hopping way between equilibrium positions; it has a well-defined threshold in a given region, but the threshold varies rather widely for different regions. The average propagation velocity increases linearly from zero with the control parameter epsilon until epsilon approximate to 2 but tends to saturate thereafter. Significantly, the drift direction reverses on switching the field polarity. The mechanism responsible for the drift appears to involve a coupling between the transverse field gradients due to the conductivity anisotropy and the transverse component of the flexoelectric polarization.