It has recently been established experimentally that the supramolecular assemblies formed by a particular class of chiral discotic molecules in solution exhibit a helical transition. To rationalize the experimental data, we apply the standard theory of linear self-assembly modified by a simple two-state model for the molecules in the aggregates, based on the Zimm-Bragg theory for the helical transition in conventional polymers. The theory provides a description of the amount of material in aggregates as well as their mean size and state of helicity as a function of the concentration of dissolved material, two binding strengths, and a parameter measuring the cooperativity of the helical transition. By fitting to the experimental data, all the model parameters are determined. It emerges that the helical transition is highly cooperative and that the growth spurt the aggregates exhibit at low temperatures is largely due to coupling of the self-assembly to the helical transition.