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.
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