  With its capacity to observe $\sim 10^{5-6}$ faint active galactic nuclei
(AGN) out to redshift $z\approx 6$, Roman is poised to reveal a population of
$10^{4-6}\, {\rm M_\odot}$ black holes during an epoch of vigorous galaxy
assembly. By measuring the light curves of a subset of these AGN and looking
for periodicity, Roman can identify several hundred massive black hole binaries
(MBHBs) with 5-12 day orbital periods, which emit copious gravitational
radiation and will inevitably merge on timescales of $10^{3-5}$ years. During
the last few months of their merger, such binaries are observable with the
Laser Interferometer Space Antenna (LISA), a joint ESA/NASA gravitational wave
mission set to launch in the mid-2030s. Roman can thus find LISA precursors,
provide uniquely robust constraints on the LISA source population, help
identify the host galaxies of LISA mergers, and unlock the potential of
multi-messenger astrophysics with massive black hole binaries.
