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 parsecs per cubic centimeter), exceptionally intense (120 ± 30 janskys), linearly polarized, scintillating burst (FRB 150807) that we directly localize to 9 square arc minutes. On the basis of a low Faraday rotation (12.0 ± 0.7 radians per square meter), we infer negligible magnetization in the circum-burst plasma and constrain the net magnetization of the cosmic web along this sightline to <21 nanogauss, parallel to the line-of-sight. The burst scintillation suggests weak turbulence in the ionized intergalactic medium.