MAGNETIC fields pervade spiral galaxies(1)--at least all those searched so far; these fields have a substantial energy density, and hence could play an important role in galaxy evolution. Dynamo theory has been used for many years to explain the presence and overall structure of galactic magnetic fields, through the amplification of a weak seed field(2,3). Here we report the observation of two ’magnetic spiral arms’ in the nearby galaxy NGC6946, lying between the optical spiral arms. This is surprising because dynamo action is thought to be related to star formation activity(4), which is concentrated within or in the leading edges of the optical spiral arms. The magnetic spiral arms are about 500-1,000 parsecs wide and more than 12 kiloparsecs long, and have greater symmetry than the optical arms. This organized structure probably reflects the signature of some global mechanism relating to magnetic field generation, but no current theory--in particular dynamo theory in its present form--is able to explain this phenomenon.