We present the internal kinematics of UCD3, the brightest known ultra-compact dwarf galaxy (UCD) in the Fornax cluster, making this the first UCD with spatially resolved spectroscopy. Our study is based on seeing-limited observations obtained with the ARGUS Integral Field Unit of the VLT/FLAMES spectrograph under excellent seeing conditions (0.5 - 0.67 arcsec FWHM). The velocity field of UCD3 shows the signature of weak rotation, comparable to that found in massive globular clusters. Its velocity dispersion profile is fully consistent with an isotropic velocity distribution and the assumption that mass follows the light distribution obtained from Hubble Space Telescope imaging. In particular, there is no evidence for the presence of an extended dark matter halo contributing a significant (>~33 per cent within R < 200 pc) mass fraction, nor for a central black hole more massive than ~5 per cent of the UCDs mass. While this result does not exclude a galaxian origin for UCD3, we conclude that its internal kinematics are fully consistent with it being a massive star cluster.
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