All-atom molecular dynamics simulations are performed on two chromonic mesogens in aqueous solution: 5,5 -dimethoxy-bis-(3,3 -di-sulphopropyl)thiacyanine triethylammonium salt (Dye A) and 5,5 -dichloro-bis-(3,3 -di-sulphopropyl)-thiacyanine triethylammonuim salt (Dye B). Simulations demonstrate the formation of self-assembled chromonic aggregates with an interlayer distance of 0.35 nm, with neighboring molecules showing a predominantly head-to-tail antiparallel stacking arrangement to minimize electrostatic repulsion between hydrophilic groups. Strong overlap of the aromatic rings occurs within the self-assembled columns, characteristic of H-aggregation in aqueous solution. At low concentrations, aggregates of Dye A form chiral columns, despite the presence of strictly achiral species. Chirality arises out of the minimization of steric repulsion between methoxy groups, which would otherwise disrupt the stacking of aromatic molecular cores. At higher concentrations, simulations suggest the interaction of short columns leads to the formation of an achiral-layered structure in which hydrophobic aromatic regions of the molecule are sandwiched between two layers of hydrophilic groups. This novel lamellar structure is suggested as a likely candidate for the structure of a J-aggregate. The latter is known to exhibit intense red-shifted absorption peaks in solution but their structure has not yet been characterized. Self-organization of such structures provides a route to the formation of "smectic" chromonic mesophases.