Chemiluminescence requires a combination of two special kinds of chemistry. The first is called fluorescence. In fluorescence, a molecule absorbs light to become excited state as a product of a chemical reaction. After a lifetime - as short as 1 billionth of a second - the energetic excited state releases its energy as light.
The second and more unusual kind of chemistry required is, of course, the chemical reaction that produces the excited state. This is called the excitation process and is the real key to chemiluminescence. We now know that certain decomposition reaction of organic peroxides can produce excited products efficiently. In addition to substantial instantaneous energy release and the formation of a fluorescent product, other more subtle requirements must be met which involve the distribution of energy released from a reaction between light emitting (or electronic) excited states and heat emitting (or vibrational) excited states.