  Fast radio bursts (FRBs) are millisecond-duration events thought to originate
beyond the Milky Way galaxy. Uncertainty surrounding the burst sources, and
their propagation through intervening plasma, has limited their use as
cosmological probes. We report on a mildly dispersed (dispersion measure
266.5+-0.1 pc cm^-3), exceptionally intense (120+-30 Jy), linearly polarized,
scintillating burst (FRB 150807) that we directly localize to 9 arcmin^2. Based
on a low Faraday rotation (12.0+-0.7 rad m^-2), we infer negligible
magnetization in the circum-burst plasma and constrain the net magnetization of
the cosmic web along this sightline to <21 nG, parallel to the line-of-sight.
The burst scintillation suggests weak turbulence in the ionized intergalactic
medium.
