Abstract The character of the probability distribution function of optical excitation in a one-dimensional random chain is discussed in the framework of the tight-binding approximation. Its dependence on the topology of the chain has been treated. For the infinite chain the excitation remains localized on the initially excited atom (molecule). For the finite chain a non-trivial probability distribution function exists depending on the character of randomness. Maxima of the probability distribution in areas of local maxima of the atomic density exist.