Plasmonic hot spots are formed when metal surfaces with high curvature are separated by nanoscale gaps and an electromagnetic field is localized within the gaps. These hot spots are responsible for phenomena such as subwavelength focusing(1,2), surface-enhanced Raman spectroscopy(3) and electromagnetic transparency(4), and depend on the geometry of the nanojunctions between the metal surfaces(5). Direct-write techniques such as electron-beam lithography can create complex nanostructures with impressive spatial control(6) but struggle to fabricate gaps on the order of a few nanometres or manufacture arrays of nanojunctions in a scalable manner. Self-assembly methods, in contrast, can be carried out on a massively parallel scale using metal nanoparticle building blocks of specific shape(7,8). Here, we show that polymer-grafted metal nanocubes can be self-assembled into arrays of one-dimensional strings that have well-defined interparticle orientations and tunable electromagnetic properties. The nanocubes are assembled within a polymer thin film and we observe unique superstructures derived from edge-edge or face-face interactions between the nanocubes. The assembly process is strongly dependent on parameters such as polymer chain length, rigidity or grafting density, and can be predicted by free energy calculations.