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We report the observation of an antipolar phase in cubic GaNb_4S_8 driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of Nb_4S_4 molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at T_JT=31 K, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in