  Following a BeppoSAX alert (Piro 1999a) and the discovery of the OT at SAAO
(Vreeswijk et al. 1999a), we observed GRB 990510 with the FORS instrument on
ESO's VLT Unit 1 (`Antu'). The burst is unremarkable in gamma rays, but in
optical is the first one to show good evidence for jet-like outflow (Stanek et
al. 1999, Harrison et al. 1999). We report the detection of significant linear
polarization in the afterglow: it is (1.6 +/- 0.2)% 0.86 days after trigger,
and after 1.81 days is consistent with that same value, but much more
uncertain. The polarization angle is constant on a time scale of hours, and may
be constant over one day. We conclude that the polarization is intrinsic to the
source and due to the synchrotron nature of the emission, and discuss the
random and ordered field geometries that may be responsible for it.
