  The recent claim by Coburn & Boggs to have detected a very high degree of
linear polarization in the prompt emission of GRB 021206 has stimulated
interest in how much polarization could arise in gamma-ray bursts from
synchrotron emission. Alternatively, as Shaviv & Dar have shown, GRB
polarization could be produced by inverse Compton scattering in the
point-source limit. We discuss polarization from a fireball that upscatters a
soft radiation field. We show that, after the proper angular integration, the
residual polarization can be large, in some cases approaching the point-source
limit. We discuss the probability of realizing the geometrical conditions in
which a large polarization is obtained showing that, for a particularly bright
burst as GRB 021206, the detection of polarization at the first attempt in the
Compton drag scenario is not unlikely.
