FU Tau belongs to a rare class of young, wide brown dwarf binaries. We have resolved the system in a Chandra X-ray observation and detected only the primary, FU Tau A. Hard X-ray emission, presumably from a corona, is present but, unexpectedly, we detect also a strong and unusually soft component from FU Tau A. Its X-ray properties, so far unique among brown dwarfs, are very similar to those of the T Tauri star TW Hya. The analogy with TW Hya suggests that the dominating soft X-ray component can be explained by emission from accretion shocks. However, the typical free-fall velocities of a brown dwarf are too low for an interpretation of the observed X-ray temperature as post-shock region. On the other hand, velocities in excess of the free-fall speed are derived from archival optical spectroscopy, and independent pieces of evidence for strong accretion in FU Tau A are found in optical photometry. The high X-ray luminosity of FU Tau A coincides with a high bolometric luminosity confirming an unexplained trend among young brown dwarfs. In fact, FU Tau A is overluminous with respect to evolutionary models while FU Tau B is on the 1 Myr isochrone suggesting non-contemporaneous formation of the two components in the binary. The extreme youth of FU Tau A could be responsible for its peculiar X-ray properties, in terms of atypical magnetic activity or accretion. Alternatively, rotation and magnetic field effects may reduce the efficiency of convection which in turn affects the effective temperature and radius of FU Tau A shifting its position in the HR diagram. Although there is no direct prove of this latter scenario so far we present arguments for its plausibility.