Aggregated cyanines form ordered supramolecular structures with the potential to transport energy efficiently over long distances, a hallmark of photosynthetic light-harvesting complexes. In concentrated aqueous solution, pseudoisocyanine (PIC) spontaneously forms fibers with a chiral J-band red-shifted 1600 cm-1 from the monomeric 0-0 transition. A cryogenic transmission electron microscopy analysis of these fibers show an average fiber width of 2.89 nm, although the molecular-level structure of the aggregate is currently unknown. To determine a molecular model for these PIC fibers, the calculated spectra and dynamics using a Frenkel exciton model are compared to experiment. A chiral aggregate model in which the PIC monomers are neither parallel nor orthogonal to the long axis of the fiber is shown to replicate the experimental spectra most closely. This model can be physically realized by the sequential binding of PIC dimers and monomers to the ends of the fiber. These insights into the molecular aggregation model for aqueous PIC can also be applied to other similar cyanine-based supramolecular complexes with the potential for long-range energy transport, a key building block for the rational design of novel excitonic systems.