  Like Hipparcos, Gaia is designed to give absolute parallaxes, independent of
any astrophysical reference system. And indeed, Gaia's internal zero-point
error for parallaxes is likely to be smaller than any individual parallax
error. Nevertheless, due in part to mechanical issues of unknown origin, there
are many astrophysical questions for which the parallax zero-point error
$\sigma(\pi_0)$ will be the fundamentally limiting constraint. These include
the distance to the Large Magellanic Cloud and the Galactic Center. We show
that by using the photometric parallax estimates for RR Lyrae stars (RRL)
within 8kpc, via the ultra-precise infrared period-luminosity relation, one can
independently determine a hyper-precise value for $\pi_{0}$. Despite their
paucity relative to bright quasars, we show that RRL are competitive due to
their order-of-magnitude improved parallax precision for each individual object
relative to bright quasars. We show that this method is mathematically robust
and well-approximated by analytic formulae over a wide range of relevant
distances.
