Aspirin (acetylsalicylic acid) has been vitrified (i) completely by melting and cooling, and (ii) partially by ball-milling at ambient temperature and then cooling. Its supercooled viscous liquid was found to be stable against crystallization for several days at 298 K even when it contained crystals. The time- and temperature-dependent changes due to its structural relaxation that occur on heating its glassy state have been studied by differential scanning calorimetry. The data have been analyzed in terms of a formalism for the non-exponential, non-linear, irreversible change of the fictive temperature, T-f, or enthalpy of its glass. The glass-softening temperature of aspirin is 244 +/-1 K, as measured for 30 K min(-1) rate. It shows a remarkably broad distribution of structural relaxation times, tau, and a relatively small non-linearity. The distribution parameter, beta, is 0.33 +/-0.04, and the non-linearity parameter, x, is 0.9. When experiments were performed in aluminium containers, or in the presence of aluminium metal, the direction of change in the heat signal reversed in the middle of the glass-softening temperature range, indicating a rapidly growing contribution from an exothermic effect. This showed that aspirin (and possibly its impurities, acetic acid and salicylic acid) reacts with the thin film of Al2O3 and Al at a rate which rapidly increases with temperature and the enthalpy of reaction is large. The reversal of the heat signal occurred at 252 +/-1 for 30 K min(-1) heating rate when tau had reached 2.5-8.5 s. This is a remarkably unusual occurrence in which the effect of a chemical reaction dominates before a viscous liquid reaches its equilibrium state. It is attributed to the unusually low value of beta and the consequent dispersion of the reaction rate constants. It is suggested that similar observations for glasses with small values of beta may help us investigate the role of molecular diffusion in dispersive kinetics of chemical reactions.