  The recently detected linear polarization in the optical lightcurve of GRB
990510 renewed the interest on how polarization can be produced in gamma-ray
burst fireballs. Here we present a model based on the assumption that we are
seeing a collimated fireball, observed slightly off-axis. This introduces some
degree of anisotropy, and makes it possible to observe a linearly polarized
flux even if the magnetic field is completely tangled in the plane orthogonal
to the line of sight. We construct the lightcurve of the polarization flux,
showing that it is always characterized by two maxima, with the polarization
position angle changing by 90 deg. between the first and the second maximum.
The very same geometry here assumed implies that the total flux initially
decays in time as a power law, but gradually steepens as the bulk Lorentz
factor of the fireball decreases.
