Fast Radio Bursts are bright , unresolved , non-repeating , broadband , millisecond flashes , found primarily at high Galactic latitudes , with dispersion measures much larger than expected for a Galactic source \cite Lorimer02112007,2012MNRAS.425L..71K , 2013Sci…341…53T , 2014ApJ…790..101S , 2014ApJ…792…19B , 2015MNRAS.447..246P,2015ApJ…799L…5R,2015arXiv151107746C . The inferred all-sky burst rate \cite 2015arXiv150500834R is comparable to the core-collapse supernova rate \cite 2014ApJ…792..135T out to redshift 0.5 . If the observed dispersion measures are assumed to be dominated by the intergalactic medium , the sources are at cosmological distances with redshifts \cite 2004MNRAS.348..999I , 2003ApJ…598L..79I of 0.2 to 1 . These parameters are consistent with a wide range of source models \cite 2014MNRAS.439L..46L,2014ApJ…797…70K , 2015ApJ…809…24G,2014MNRAS.442L…9L,2014A Align A…562A.137F,2015arXiv150505535C . One fast radio burst \cite 2015MNRAS.447..246P showed circular polarization [ 21 ( 7 ) % ] of the radio emission , but no linear polarization was detected , and hence no Faraday rotation measure could be determined . Here we report the examination of archival data revealing Faraday rotation in a newly detected burst—FRB 110523 . It has radio flux at least 0.6 Jy and dispersion measure 623.30 ( 5 ) pc cm ^ { -3 } . Using Galactic contribution 45 pc cm ^ { -3 } and a model of intergalactic electron density \cite 2004MNRAS.348..999I , we place the source at a maximum redshift of 0.5 . The burst has rotation measure –186.1 ( 1.4 ) rad m ^ { -2 } , much higher than expected for this line of sight through the Milky Way and the intergalactic medium , indicating magnetization in the vicinity of the source itself or within a host galaxy . The pulse was scattered by two distinct plasma screens during propagation , which requires either a dense nebula associated with the source or a location within the central region of its host galaxy . Keeping in mind that there may be more than one type of fast radio burst source , the detection in this instance of source-local magnetization and scattering favours models involving young stellar populations such as magnetars over models involving the mergers of older neutron stars , which are more likely to be located in low density regions of the host galaxy .