We report the results of a computational study of the mechanism of the light-induced chemical reaction of chromophore hydration in the fluorescent protein Dreiklang, responsible for its switching from the fluorescent ON-state to the dark OFF-state. We explore the relief of the charge-transfer excited-state potential energy surface in the ON-state to locate minimum energy conical intersection points with the ground-state energy surface. Simulations of the further evolution of model systems allow us to characterize the ground-state reaction intermediate tentatively suggested in the femtosecond studies of the light-induced dynamics in Dreiklang and finally to arrive at the reaction product. The obtained results clarify the details of the photoswitching mechanism in Dreiklang, which is governed by the chemical modification of its chromophore.