  The accretion disks of active galactic nuclei (AGN) are promising locations
for the merger of compact objects detected by gravitational wave (GW)
observatories. Embedded within a baryon-rich, high density environment, mergers
within AGN are the only GW channel where an electromagnetic (EM) counterpart
must occur (whether detectable or not). Considering AGN with unusual flaring
activity observed by the Zwicky Transient Facility (ZTF), we describe a search
for candidate EM counterparts to binary black hole (BBH) mergers detected by
LIGO/Virgo in O3. After removing probable false positives, we find nine
candidate counterparts to BBH mergers mergers during O3 (seven in O3a, two in
O3b) with a $p$-value of 0.019. Based on ZTF sky coverage, AGN geometry, and
merger geometry, we expect $\approx 3(N_{\rm BBH}/83)(f_{\rm AGN}/0.5)$
potentially detectable EM counterparts from O3, where $N_{\rm BBH}$ is the
total number of observed BBH mergers and $f_{\rm AGN}$ is the fraction
originating in AGN. Further modeling of breakout and flaring phenomena in AGN
disks is required to reduce our false positive rate. Two of the events are also
associated with mergers with total masses $> 100M_\odot$, which is the expected
rate for O3 if hierarchical (large mass) mergers occur in the AGN channel.
Candidate EM counterparts in future GW observing runs can be better constrained
by coverage of the Southern sky as well as spectral monitoring of unusual AGN
flaring events in LIGO/Virgo alert volumes. A future set of reliable AGN EM
counterparts to BBH mergers will yield an independent means of measuring cosmic
expansion ($H_0$) as a function of redshift.
