Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows.