Nature's highly efficient light-harvesting antennae, such as those found in green sulfur bacteria, consist of supramolecular building blocks that self-assemble into a hierarchy of close-packed structures. In an effort to mimic the fundamental processes that govern nature's efficient systems, it is important to elucidate the role of each level of hierarchy: from molecule, to supramolecular building block, to close-packed building blocks. Here, we study the impact of hierarchical structure. We present a model system that mirrors nature's complexity: cylinders self-assembled from cyanine-dye molecules. Our work reveals that even though close-packing may alter the cylinders' soft mesoscopic structure, robust delocalized excitons are retained: Internal order and strong excitation-transfer interactions-prerequisites for efficient energy transport-are both maintained. Our results suggest that the cylindrical geometry strongly favors robust excitons; it presents a rational design that is potentially key to nature's high efficiency, allowing construction of efficient light-harvesting devices even from soft, supramolecular materials.