We have formulated the exciton dynamics in a disordered linear chain with exciton wave functions given by the one-dimensional Frenkel exciton Hamiltonian with disorder. It is assumed that exciton-phonon coupling is weak and that the dynamics is governed by the competing processes of phonon scattering and radiative decay. The phonon scattering rate is given on the assumption that excitons do not change the site by the scattering. The strength of exciton-phonon coupling and the density of phonon states are independent of energy. The radiative decay rate is given by the Einstein's A coefficient. The detail of the numerical procedure is also described. Absorption spectra, luminescence spectra, the time response of luminescence intensity, and temperature dependence are calculated for the model system of poly(di-n-hexylsilane) film. It is discussed that long-range dipole-dipole interaction is responsible for the luminescence depolarization. (C) 2001 American Institute of Physics.