Förster resonant energy transfer (FRET) can be an efficient energy transfer mechanism between densely packed fluorescent emitters. It plays a key role in photosynthesis but may also be detrimental. In optoelectronic devices for instance, FRET funnels energy to quenching sites and favors losses. Here, we image individual self-assembled chains of stacked CdSe nanoplatelets and demonstrate fluorescence intermittency (blinking) of chain portions corresponding to a few tens of platelets. This collective blinking is attributed to the fluctuations of a quencher site, to which excitons are transferred by FRET migration from the surrounding platelets. We develop an analytical random walk model of the chain and show that an ensemble of platelets can be quenched collectively by a single site provided that its quenching (nonradiative recombination) rate is faster than the geometric mean of the radiative recombination rate and the transfer rate, which for self-assembled platelets would be of the order of (100 ps)⁻¹.