Fluorophores that emit in the near-infrared (NIR, 700-1700 nm) and have high quantum yields are urgently needed for many technical applications such as organic light-emitting diodes or bioimaging. The design of such chromophores is hampered by the energy gap law, which states that shifting the emission to lower wavelengths is accompanied by a dramatic increase in the nonradiative decay rate. In this article we argue that linear oligomers with J-type excitonic coupling are ideal NIR fluorophores because of the advantageous dependence of the emission energy and the radiative and nonradiative rates on the length N over which the excitation is delocalized. The lowering of the emission energy due to exciton splitting and the linear increase of the radiative rate with length (super-radiance) are well understood. However, less attention has been paid to the decrease of the nonradiative rate with length, which can compensate for the exponential increase due to the energy gap law. According to the exciton model, the Huang-Rhys factors decrease like N-2 while the strength of the nonadiabatic coupling remains approximately constant. Plugging these relations into the Englman-Jortner's energy gap law, we show that for excitonic coupling that is not too strong the nonradiative rate decreases quickly with N. This phenomenon explains the decrease of the nonradiative rate with length in J-aggregates of carbocyanine dyes and the exceptionally high fluorescence quantum yields of linear ethyne-linked zinc-porphyrin arrays, which seemed to defy the energy gap law.