  Intensity interferometry is a technique developed many decades ago, that has
recently enjoyed a renaissance thanks in part to advances in photodetector
technology. We investigate the potential for long-baseline optical intensity
interferometry to observe bright, active galactic nuclei (AGN) associated with
rapidly accreting supermassive black holes. We argue that realistic telescope
arrays similar in area to existing Cherenkov arrays, if equipped with modern
high-precision single photon detectors, can achieve a sufficiently high signal
to noise ratio not only to detect distant AGN, but also to study them in great
detail. We explore the science potential of such observations by considering
two examples. First, we find that intensity interferometric observations of
bright nearby AGN can allow detailed studies of the central accretion disks
powering the AGN, allowing reconstruction of many disk properties like the
radial profile. Next, we argue that intensity interferometers can spatially
resolve the broad-line regions of AGN at cosmological distances, and thereby
provide a geometric determination of the angular diameter distances to those
AGN when combined with reverberation mapping. Since this measurement can be
performed for AGN at distances of hundreds of megaparsecs, this directly
measures the Hubble expansion rate $H_0$, with a precision adequate to resolve
the recent Hubble tension. Finally, we speculate on future applications that
would be enabled by even larger intensity interferometer arrays.
