  Off-nucleus active galactic nuclei (AGN) can be signposts of inspiraling
supermassive black holes (SMBHs) on galactic scales, or accreting SMBHs
recoiling after the coalescence of a SMBH binary or slingshot from three-body
interactions. Because of the stochastic variability of AGN, the measured
photocenter of an unresolved AGN-host system will display astrometric jitter
that depends on the off-nucleus distance of the AGN, the total photometric
variability of the system, and the AGN-host contrast. Here we use the precision
astrometry from Gaia DR2 to constrain the off-nucleus population of a
low-redshift (0.3<z<0.8) sample of unobscured broad-line AGN drawn from the
SDSS with significant host contribution and photometric variability. We find
that Gaia DR2 already provides strong constraints on the projected off-nucleus
distance in the sub-kpc regime at these redshifts: 99%, 90% and 40% of AGN must
be well-centered to <1 kpc, <500 pc and <100 pc, respectively. Limiting the
sample to the most variable subset constrains >99% of AGN to be well-centered
below 500 parsec. These results suggest that genuine off-nucleus AGN (offset by
> a few hundred pc) must be rare at low redshift. Future Gaia releases of time
series of photocenter and flux measurements, improved treatments for extended
sources and longer baselines will further tighten these constraints, and enable
a systematic full-sky search for rare off-nucleus AGN on ~ 10-1000 pc scales.
