ABSTRACT Magnetic fields play an important role in the evolution of galaxies and in shaping the dynamics of their interstellar medium. However, the formation history of magnetic fields from initial seed-fields to well-ordered systems is not clear. Favoured scenarios include a turbulent dynamo that amplifies the field, and a mean-field dynamo that organizes it. Such a model can be tested through observing the magnetic-field structure of galaxies in the early Universe given the relative formation time-scales involved. Here, we combine the high angular resolution of the Atacama Large Millimetre Array (ALMA) and gravitational lensing to resolve the magnetic field structure of a 4 kpc in extent grand-design spiral when the Universe was just 2.6 Gyr old. We find that the spiral arm structure, as traced by the heated dust emission, is coincident with the linearly polarized emission, which is consistent with a highly ordered magnetic field. The time-scale needed to produce such an ordered field is likely within at least several rotations of the disc. Our study highlights the importance of combining the long baselines of ALMA and gravitational lensing to resolve the structure of galaxies at cosmologically interesting epochs.