The natural structure for smectic-A liquid crystals arranged in a sample with homogeneous boundary conditions is the so-called bookshelf structure with uniform layers perpendicular to the sample cell plane. However, this structure often deforms into the so-called chevron structure when the sample is cooled. This deformation is usually thought to result from the mismatch between bulk and surface layer thicknesses. In this paper we study the dynamics of chevron formation. Two possible scenarios are envisaged. In one of these there is strong coupling between layer deformation and fluid flow, and in the other the fluid essentially does not move. In this paper we examine the first scenario, leaving the second, slower relaxation mode for another paper. Analytic solutions are found for near-critical deformations, and numerical solutions are found beyond the critical regime.