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We study phase synchronization in a chain of weakly coupled chaotic oscillators. In the synchronous state, the phases of oscillators are locked, while the amplitudes remain chaotic. We demonstrate that the coexistence of several clusters of mutually synchronized elements and global synchronization of all oscillators is possible. Two mechanisms of the transition to global synchronization are shown. The dynamics of spatiotemporal defects is discussed for the cases of phase-coherent and funnel Rössler oscillators.