  The Galactic Center was observed at 8.6 mum in order to detect a mid-infrared
(MIR) counterpart of Sgr A*, parallel to NIR observations. The goal was to set
constraints on possible emission mechanisms.Imaging data were acquired with the
adaptive optics assisted NIR instrument NACO and the MIR instrument VISIR at
the ESO VLT. We present MIR imaging data of an unprecedented quality in terms
of spatial resolution and sensitivity. An extended ridge of emission is found
to be present in the immediate vicinity of Sgr A* and thus renders any
detection of a point source difficult. No MIR point source related to Sgr A*
was detected during the observations. We derive a tight upper limit of 22+-4
mJy (dereddened) on any possible point source present during the observations
in the night of 4/5 June 2006. The absence of a flare in simultaneous
observations at 2.2 mum and the low limits on any possible variability in the
MIR suggest strongly that Sgr A* was in a quasi-quiescent state during this
night. During the night from 5 to 6 June 2006, Sgr A* was found to be variable
on a low level at 3.8 mum. No point source at 8.6 mum was detected during the
simultaneous MIR observations. Due to the poorer atmospheric conditions a
higher upper limit of 60+-30mJy was found for Sgr A* at 8.6 mum during the
second night. The observations are consistent with theoretical predictions. If
the published models are correct, the observations demonstrate successfully
that a 8.6 mum counterpart of Sgr A* can be easily detected in its flaring
state. Spectral indices derived from simultaneous observations of flaring
emission from Sgr A* at NIR and MIR wavelengths will enable us to distinguish
between different kinds of flare models.
