Surface-directed spinodal decomposition (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a surface-registry regime to a phase-separation regime. We study this crossover using layerwise correlation functions and structure factors and domain length scales. © 2020 American Physical Society.