  We compared positions of the Gaia first data release (DR1) secondary data set
at its faint limit with CCD positions of stars in 20 fields observed with the
VLT/FORS2 camera. The FORS2 position uncertainties are smaller than one
milli-arcsecond (mas) and allowed us to perform an independent verification of
the DR1 astrometric precision. In the fields that we observed with FORS2, we
projected the Gaia DR1 positions into the CCD plane, performed a polynomial fit
between the two sets of matching stars, and carried out statistical analyses of
the residuals in positions. The residual RMS roughly matches the expectations
given by the Gaia DR1 uncertainties, where we identified three regimes in terms
of Gaia DR1 precision: for G = 17-20 stars we found that the formal DR1
position uncertainties of stars with DR1 precisions in the range of 0.5-5 mas
are underestimated by 63 +/- 5\%, whereas the DR1 uncertainties of stars in the
range 7-10 mas are overestimated by a factor of two. For the best-measured and
generally brighter G = 16-18 stars with DR1 positional uncertainties of <0.5
mas, we detected 0.44 +/- 0.13 mas excess noise in the residual RMS, whose
origin can be in both FORS2 and Gaia DR1. By adopting Gaia DR1 as the absolute
reference frame we refined the pixel scale determination of FORS2, leading to
minor updates to the parallaxes of 20 ultracool dwarfs that we published
previously. We also updated the FORS2 absolute parallax of the Luhman 16 binary
brown dwarf system to 501.42 +/- 0.11 mas
