The energy for chemiluminscence comes from the oxidation of oxalic phthalate ester with hydrogen peroxide The phthalate ester is the solution in the main part of the lightstick, and the hydrogen peroxide is in the glass ampule that breaks.
An intermediate is formed during the oxidation that has a high energy four membered ring. The breakdown of this intermediate passes energy to a dye molecule, placing the dye molecule in an excited electronic state. The dye molecule fluoresces, returning to its ground state, thus producing the light from the lightstick.
If the dye molecule can be placed in its excited state through some other means, such as laser excitation the lightstick will produce the same light.