A novel complex nanostructure, produced by the directed assembly of a block copolymer thin film on chemically patterned surfaces, is presented. The new nanostructure, which consists of cylinders oriented alternately parallel and perpendicular to the surface (see figure, a result of self-consistent field calculations), demonstrates that a judiciously designed chemical pattern may be used to fabricate a well-ordered complex nanostructure in block copolymer thin films.