It is well known that chemically patterned substrates can direct the assembly of adsorbed layers or thin films of block copolymers. For a cylinder-forming diblock copolymer on periodically spot-patterned substrates, the morphology of the block copolymer follows the pattern at the substrate; however, with different periodic spacing and spot size of the pattern, novel morphologies can be created. Specifically, we have demonstrated that new morphologies that are absent in the bulk system can be tailored by judiciously varying the mismatch between the width of the pattern and the periodic spacing of the bulk block copolymer, the top surface affinity, and spot size. New morphologies can thus be achieved, such as honeycomb and ring structures, which do not appear in the bulk system. These results demonstrate a promising strategy for fabrication of new nanostructures from chemically patterned substrates.