We present spatially-resolved, rest-frame optical spectroscopy of a z˜ 3 Lyman-break galaxy (LBG), Q0347-383 C5, obtained with SINFONI on the VLT. This galaxy, among the ˜ 10% brightest LBGs, is only the second z˜ 3 LBG observed with an integral-field spectrograph. It was first described by Pettini et al. (2001, ApJ, 554, 981), who obtained WFPC2 F702W imaging and longslit spectroscopy in the K-band. We find that the emission line morphology is dominated by two unresolved blobs at a projected distance of ˜ 5 kpc with a velocity offset of ˜ 33 km s^-1. Velocity dispersions suggest that each blob has a mass of ˜ 10¹⁰ M_&sun;. Unlike Pettini et al. (2001), our spectra are deep enough to detect Hbeta, and we derive star-formation rates of ˜ 20{-}40 M_&sun; yr^-1, and use the Hbeta/[OIII] ratio to crudely estimate an oxygen abundance 12+[O/H]=7.9{-}8.6, which is in the range typically observed for LBGs. We compare the properties of Q0347-383 C5 with what is found for other LBGs, including the gravitationally lensed ``arc+core'' galaxy (Nesvadba et al. 2006, ApJ, 650, 661), and discuss possible scenarios for the nature of the source, namely disk rotation, a starburst-driven wind, disk fragmentation, and merging of two LBGs. We favor the merging interpretation for bright, extended LBGs like Q0347-383 C5, in broad agreement with predicted merger rates from hierarchical models.