  Galaxies are believed to evolve through merging, which should lead to
multiple supermassive black holes in some. There are four known triple black
hole systems, with the closest pair being 2.4 kiloparsecs apart (the third
component is more distant at 3 kiloparsecs), which is far from the
gravitational sphere of influence of a black hole with mass $\sim$10$^9$
M$_\odot$ (about 100 parsecs). Previous searches for compact black hole systems
concluded that they were rare, with the tightest binary system having a
separation of 7 parsecs. Here we report observations of a triple black hole
system at redshift z=0.39, with the closest pair separated by $\sim$140
parsecs. The presence of the tight pair is imprinted onto the properties of the
large-scale radio jets, as a rotationally-symmetric helical modulation, which
provides a useful way to search for other tight pairs without needing extremely
high resolution observations. As we found this tight pair after searching only
six galaxies, we conclude that tight pairs are more common than hitherto
believed, which is an important observational constraint for low-frequency
gravitational wave experiments.
