A precursor of a strong first-order structural phase transition has been detected as the critical speeding-up of the lifetime of the fluorescence excited by a picosecond pulsed laser. In the alpha - beta transition of a resorcinol (C₆H₄(OH)₂) crystal, a critical decrease of the lifetimes and an increase in the intensity of the impurity-induced fluorescence were found from about 30 K below T_c. This is in contrast with the fact that the temperature dependence of the Raman spectra and the dielectric constant shows no precursor effect. From a detailed polarization study, large-amplitude and short-lived vibrational fluctuations associated with the phase transition are suggested as a possible origin of the precursor. Despite the apparent contradiction of the fluctuation-dissipation theorem, the results indicate that divergence of the fluctuation also takes place in the first-order phase transition. The method provides a new approach to the study of a first-order phase transition.