  Linear polarization at the level of $\sim 1-3%$ has by now been measured in
several gamma-ray burst afterglows. Whereas the degree of polarization, $P$,
was found to vary in some sources, the position angle, $\theta_p$, was roughly
constant in all cases. Until now, the polarization has been commonly attributed
to synchrotron radiation from a jet with a tangled magnetic field that is
viewed somewhat off axis. However, this model predicts either a peak in $P$ or
a $90^\circ$ change in $\theta_p$ around the ``jet break'' time in the
lightcurve, for which there has so far been no observational confirmation. We
propose an alternative interpretation, wherein the polarization is attributed,
at least in part, to a large-scale, ordered magnetic field in the ambient
medium. The ordered component may dominate the polarization even if the total
emissivity is dominated by a tangled field generated by postshock turbulence.
In this picture, $\theta_p$ is roughly constant because of the uniformity of
the field, whereas $P$ varies as a result of changes in the ratio of the
ordered-to-random mean-squared field amplitudes. We point out that variable
afterglow light curves should be accompanied by a variable polarization. The
radiation from the original ejecta, which includes the prompt gamma-ray
emission and the emission from the reverse shock (the `optical flash' and
`radio flare'), could potentially exhibit a high degree of polarization (up to
$\sim 60%$) induced by an ordered transverse magnetic field advected from the
central source.
