We consider a film of SmC* liquid crystal with its layers parallel to an applied electric field. The liquid crystal is assumed to align uniformly under the influence of the field, except along domain walls. By employing a nonlinear continuum theory for smectic liquid crystals we can examine the width of domain walls perpendicular and parallel to the field. We obtain predictions for the wall widths based on the elastic constants and dielectric properties of the SmC* liquid crystal. Exact analytical expressions for the wall widths are obtained by assuming series expansions in the elastic anisotropy and dielectric parameters.