Luminescence decay of thin solid films of molecular chlorine exhibit distinctly non-exponential temporal behavior following pulsed ultraviolet laser excitation. The temporal characteristics are dependent on sample temperature and laser fluence in the range 11-80 K. This behavior is attributed to internal conversion from the first excited A'((II2u)-I-3) electronic state to the ground state, which is accelerated by phonons and localized vibrational excitons (vibrons). This unusual mechanism of electronic relaxation is consistent with a recent theoretical model for the mechanism of explosive desorption of cryogenic films.