  We present an investigation of the stability of the two chips in the FORS2
camera CCD mosaic on the basis of astrometric observations of stars in 20 sky
fields, some of which were monitored for four to seven years. We detected a
smooth relative shear motion of the chips along their dividing line that is
well approximated by a cubic function of time with an amplitude that reaches
~0.3 pixels (px) or ~38 mas over seven years. In a single case, we detected a
step change of ~0.06 px that occurred within four days. In the orthogonal
direction that corresponds to the separation between the chips, the motion is a
factor of 5-10 smaller. This chip instability in the camera significantly
reduces the astrometric precision when the reduction uses reference stars
located in both chips, and the effect is not accounted for explicitly. We found
that the instability introduces a bias in stellar positions with an amplitude
that increases with the observation time span. When our reduction methods and
FORS2 images are used, it affects stellar positions like an excess random noise
with an RMS of ~0.5 mas for a time span of three to seven years when left
uncorrected. We demonstrate that an additional calibration step can adequately
mitigate this and restore an astrometric accuracy of 0.12 mas, which is
essential to achieve the goals of our planet-search program. These results
indicate that similar instabilities could critically affect the astrometric
performance of other large ground-based telescopes and extremely large
telescopes that are equipped with large-format multi-chip detectors if no
precautions are taken.
