We report a study on directed self-assembly (DSA) with solvent annealing to induce the formation of non-bulk block copolymer microdomains on chemical patterns. Ultrathin films of symmetric polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) display morphologies of PMMA dots, stripes, and PS hexagons with increasing exposure time to acetone vapor, a PMMA-selective solvent. All three nanostructures form long-range-ordered and registered arrays on striped chemical patterns with periods (LS) commensurate to the solvated PS-b-PMMA microdomain period (L0,s). Solvent annealing is shown to facilitate DSA on non-regular chemical patterns, on which the local periods are incommensurate to L0,s. DSA with feature density multiplication, via solvent annealing, is also demonstrated.