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In this work, we used scanning electron microscopy (SEM), in situ coherent small angle x-ray scattering (SAXS), and Monte Carlo molecular simulation to gain insights into the dynamics of block copolymer directed assembly with density multiplication on chemically patterned surfaces. During directed assembly, it was observed with SEM that poly(styrene-block-methyl methacrylate) initially formed discrete polystyrene domains that lacked long-range order at the free surface. After further annealing, the polystyrene domains gradually coalesced into linear domains that were not registered fully with the underlying chemical pattern. The linear domains could be trapped in metastable morphologies. Finally, the linear polystyrene domains formed perpendicular lamellae in full registration with the underlying chemical pattern. It was revealed with SAXS that scattering peaks characteristic of the period of the chemical pattern appeared and disappeared at the early stages of assembly. Finally, the morphological evolution of directed assembly of block copolymer on chemically patterned surfaces was modeled by molecular simulations.