Self-assembling materials spontaneously form structures at length scales of interest in nanotechnology. In the particular case of block copolymers, the thermodynamic driving forces for self-assembly are small, and low-energy defects can get easily trapped. We directed the assembly of defect-free arrays of isolated block copolymer domains at densities up to 1 terabit per square inch on chemically patterned surfaces. In comparing the assembled structures to the chemical pattern, the density is increased by a factor of four, the size is reduced by a factor of two, and the dimensional uniformity is vastly improved.