  The origin of ultracompact dwarfs (UCDs), a class of compact stellar systems
discovered two decades ago, still remains a matter of debate. Recent
discoveries of central supermassive black holes in UCDs likely inherited from
their massive progenitor galaxies provide support for the tidal stripping
hypothesis. At the same time, on statistical grounds, some massive UCDs might
be representatives of the high luminosity tail of the globular cluster
luminosity function. Here we present a detection of a
$3.3^{+1.4}_{-1.2}\times10^6\,M_{\odot}$ black hole ($1\sigma$ uncertainty) in
the centre of the UCD3 galaxy in the Fornax cluster, that corresponds to 4 per
cent of its stellar mass. We performed isotropic Jeans dynamical modelling of
UCD3 using internal kinematics derived from adaptive optics assisted
observations with the SINFONI spectrograph and seeing limited data collected
with the FLAMES spectrograph at the ESO VLT. We rule out the zero black hole
mass at the $3\sigma$ confidence level when adopting a mass-to-light ratio
inferred from stellar populations. This is the fourth supermassive black hole
found in a UCD and the first one in the Fornax cluster. Similarly to other
known UCDs that harbour black holes, UCD3 hosts metal rich stars enhanced in
$\alpha$-elements that supports the tidal stripping of a massive progenitor as
its likely formation scenario. We estimate that up to 80 per cent of luminous
UCDs in galaxy clusters host central black holes. This fraction should be lower
for UCDs in groups, because their progenitors are more likely to be dwarf
galaxies, which do not tend to host central black holes.
