We show that colloidal nanoplatelets can self-assemble to form a 1D superlattice. When self-assembled, an additional emission line appears in the photoluminescence spectrum at low temperatures. This emission line is a collective effect, greatly enhanced when the NPLs are self-assembled. It is attributed to the longitudinal optical (LO) phonon replica of the band-edge exciton, and its presence in self-assembled nanoplatelets is explained using a model based on an efficient photons reabsorption between neighboring nanoplatelets. The presence of phonon replica at low temperatures in ensemble measurements suggests the possibility to design a laser, based on self-assembled nanoplatelets.