  Polarization measurements provide direct insight into the nature of
astrophysical processes. Unfortunately, only a few instruments are available
for this kind of measurements at gamma-ray energies, and the sources need to be
very bright. Gamma-Ray Bursts (GRBs) are ideal candidates due to their large
flux over limited time intervals, maximizing the available signal-to-noise
ratio. To date a few polarization measurements have been reported, claiming of
a high degree of polarization in the prompt emission of GRBs but with low
statistical evidence.
  We used the IBIS telescope on board the INTEGRAL satellite to measure the
polarization of the prompt gamma-ray emission of the long and bright GRB
041219A in the 200-800 keV energy band. We find a variable degree of
polarization ranging from less than 4% over the first peak to 43+/-25% for the
whole second peak. Time resolved analysis of both peaks indicates a high degree
of polarization, and the null average polarization in the first peak can be
explained by the rapid variations observed in the polarization angle and
degree.
  Our results are consistent with different models for the prompt emission of
GRBs at these energies, but they favor synchrotron radiation from a
relativistic outflow with a magnetic field which is coherent on an angular size
comparable with the angular size of the emitting region (~1/Gamma) . Indeed
this model has the best capabilities to maintain a high polarization level, and
to produce the observed variability.
