We present a detailed reconstruction of the star-formation history of the Constellation III region in the Large Magellanic Cloud, to constrain the formation mechanism of this enigmatic feature. Star formation in Constellation III seems to have taken place during two distinct epochs: there is the 8–15 Myr epoch that had previously been recognized, but we also see strong evidence for a separate ‘burst’ of star formation 25–30 Myr ago. The ‘super-supernova' or GRB blast wave model for the formation of Constellation III is difficult to reconcile with such an extended, two-epoch star formation history, because the shock wave should have induced star formation throughout the structure simultaneously, and any unconsumed gas would quickly be dissipated, leaving nothing from which to form a subsequent burst of activity. We propose a ‘truly stochastic’ self-propagating star formation model, distinct from the canonical model in which star formation proceeds in a radially directed wave from the center of Constellation III to its perimeter. As others have noted, and we now confirm, the bulk age gradients demanded by such a model are simply not present in Constellation III. In our scenario, the prestellar gas is somehow pushed into these large-scale arc structures, without simultaneously triggering immediate and violent star formation throughout the structure. Rather, star formation proceeds in the arc according to the local physical conditions of the gas. Self-propagating star formation is certainly possible, but in a truly stochastic manner, without a directed, large scale pattern.