We investigate theoretically the phenomenon of exchange narrowing in the absorption spectrum of a chain of monomers, which are coupled via resonant dipole-dipole interaction. The individual (uncoupled) monomers exhibit a broad absorption line shape due to the coupling to an environment consisting of a continuum of vibrational modes. Upon increasing the interaction between the monomers, the absorption spectrum of the chain narrows. For a non-Markovian environment with a Lorentzian spectral density, we find a narrowing of the peak width [full width at half maximum (FWHM)] by a factor 1∕N, where N is the number of monomers. This is much stronger than the usual 1/√N narrowing. Furthermore, it turns out that for a Markovian environment no exchange narrowing at all occurs. The relation of different measures of the width (FWHM, standard deviation) is discussed.