  We measure the polarization of a photon gas in a dye-filled microcavity. The
polarization is obtained by a single-shot measurement of the Stokes parameters.
We find that the polarization of both the thermal cloud and the Bose-Einstein
condensate of photons (phBEC) does not differ from shot to shot. In the case of
the phBEC, we find that the polarization correlates with the polarization of
the pump pulse. The polarization of the thermal cloud is independent of
parameters varied in the experiment and is governed by a hidden anisotropy in
the system.
