Models for gamma-ray burst afterglows envisage an hyper-relativistic fireba
ll that is decelerated in the ambient medium around the explosion site. Thi
s interaction produces a shock wave which amplifies the magnetic field and
accelerates electrons to relativistic energies, setting the conditions for
an efficient production of synchrotron photons. If produced in a region of
large-scale ordered magnetic field, synchrotron radiation can be highly pol
arized. The optical transient associated with GRB 990510 was observed simil
ar to 18.5 hr after the event and linear polarization in the R band was mea
sured at a level of 1.7 +/- 0.2%. This is the first detection of linear pol
arization in the optical afterglow of a gamma-ray burst. We exclude that th
is polarization is due to dust in the interstellar material, either in our
Galaxy or in the host galaxy of the gamma-ray burst. These results provide
important new evidence in favor of the synchrotron origin of the afterglow
emission, and constrains the geometry of the fireball and/or magnetic field
lines.