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The youngest super star clusters (SSCs) in the Antennae Galaxies (NGC 4038/39) drive supersonic mass-loaded outflows. High-resolution Keck/NIRSPEC spectroscopy reveals broad, spatially extended Brγ emission lines that are well-fit by simple wind models. Cluster mass-loss rates are up to 1.5 M⊙ yr−1 and terminal velocities are up to 205 km s−1. These emission-line clusters (ELCs) constitute at least 15% of the star formation rate in the Antennae, and their high star formation efficiencies imply that they will probably evolve into bound SSCs. The youngest ELC outflows are driven primarily by stellar winds, and they efficiently entrain ambient matter. They transfer or dissipate most of their energy and momentum in a hot or cool medium that does not emit Brγ. ELCs are the individual engines that power galactic-scale superwinds, viewed in their earliest evolutionary stage.