VLT images in BVI are used to identify the ionizing source centered on Sersic 13, the largest HII region of the giant nearby galaxy NGC 5128 with log L_Halpha=39.6 erg/s. This ionizing source turns out to be a close pair of bright and blue star cluster candidates. Spectroscopy obtained with the Magellan I telescope confirms that these are massive young clusters physically associated with the giant HII region Sersic 13. The spectra of both clusters show prominent Wolf-Rayet type emission features, and prominent lines of HI and HeI, indicative of a very young age (t ~ few x 10^6 yr). Their luminosities make each of them at least as luminous as the massive young cluster R136 in 30 Doradus in the LMC, and their individual masses are estimated to be 1-7.5x10^5 M_sun. In addition, the projected separation of the cluster pair is 42 pc. The measured velocity difference between the clusters is small, Delta V=49+/-21 km/s, and within 2 sigma of the expected orbital velocity V_orb=5-12 km/s if they are bound. Dynamical models predict that binary clusters with these properties would merge in a short timescale of a few orbital periods (P=20-50x10^6 yr). The discovery of this binary cluster suggests that mergers of young massive clusters could lead to the formation of the most massive globular clusters such as omega Cen in our Galaxy and G1 in M31. Alternatively, if they are not gravitationally bound, these objects would individually evolve into two normal globular clusters.
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