We experimentally investigate the transition to synchronization in a population of photochemical oscillators with weak global coupling. Above a critical coupling strength the oscillators join a one-phase group or two-phase clusters. The number of oscillators in each cluster depends on the initial phase distribution, and irregular switching of oscillators between clusters is observed. The fully synchronized state emerges above a second critical coupling strength. In agreement with earlier theory, the experiments demonstrate the importance of population heterogeneity in cluster multistability.