ABSTRACT Gravitational waves from neutron star mergers have long been considered a promising way to measure the Hubble constant, H0, which describes the local expansion rate of the Universe. While black hole mergers are more abundantly observed, their expected lack of electromagnetic emission and poor gravitational-wave localization make them less well suited for measuring H0. Black hole mergers within the discs of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGN disc may produce an electromagnetic signal, pointing observers to the host galaxy. Alternatively, the low number density of AGNs could help identify the host galaxy of $1{\!-\!}5~{{\ \rm per\ cent}}$ of mergers. Here we show that black hole mergers in AGN discs may be a sensitive way to determine H0 with gravitational waves. If 1 per cent (10 per cent) of LIGO’s observations occur in AGN discs with identified host galaxies, we could measure H0 with 12 per cent (4 per cent) uncertainty in five years, possibly comparable to the sensitivity of neutron star mergers and set to considerably improve current gravitational wave measurements.