Self-assembly provides the ability to create well-controlled nanostructures with electronic or chemical functionality and enables the synthesis of a wide range of useful devices. Diblock copolymers self-assemble into periodic arrays of microdomains with feature sizes of typically 10-50 nm, and have been used to make a wide range of devices such as silicon capacitors and transistors, photonic crystals, and patterned magnetic media(1-3). However, the cylindrical or spherical microdomains in diblock copolymers generally form close-packed structures with hexagonal symmetry, limiting their device applications. Here we demonstrate self-assembly of square-symmetry patterns from a triblock terpolymer in which one organometallic block imparts high etch selectivity and etch resistance. Long-range order is imposed on the microdomain arrays by self-assembly on topographical substrates, and the orientation of both square lattices and in-plane cylinders is controlled by the substrate chemistry. Pattern transfer is demonstrated by making an array of square-packed 30 nm tall, 20 nm diameter silica pillars. Templated self-assembly of triblock terpolymers can generate nanostructures with geometries that are unattainable from diblock copolymers, significantly enhancing the capabilities of block copolymer lithography.