We report on the discovery of a new fast radio burst (FRB), FRB 150215, with the Parkes radio telescope on 2015 February 15. The burst was detected in real time with a dispersion measure (DM) of 1105.6 ± 0.8 pc cm-3, a pulse duration of 2.8^{+1.2}_{-0.5} ms, and a measured peak flux density assuming that the burst was at beam centre of 0.7^{+0.2}_{-0.1} Jy. The FRB originated at a Galactic longitude and latitude of 24.66°, 5.28° and 25° away from the Galactic Center. The burst was found to be 43 ± 5 per cent linearly polarized with a rotation measure (RM) in the range -9 < RM < 12 rad m-2 (95 per cent confidence level), consistent with zero. The burst was followed up with 11 telescopes to search for radio, optical, X-ray, γ-ray and neutrino emission. Neither transient nor variable emission was found to be associated with the burst and no repeat pulses have been observed in 17.25 h of observing. The sightline to the burst is close to the Galactic plane and the observed physical properties of FRB 150215 demonstrate the existence of sight lines of anomalously low RM for a given electron column density. The Galactic RM foreground may approach a null value due to magnetic field reversals along the line of sight, a decreased total electron column density from the Milky Way, or some combination of these effects. A lower Galactic DM contribution might explain why this burst was detectable whereas previous searches at low latitude have had lower detection rates than those out of the plane.