We show that, during false vacuum inflation, a primordial magnetic field can be created, sufficiently strong to seed the galactic dynamo and generate the observed galactic magnetic fields. Considering the inflaton dominated regime, our field is produced by the Higgs-field gradients, resulting from a grand unified phase transition. The evolution of the field is followed from its creation through to the epoch of structure formation, subject to the relevant constraints. We find that it is possible to create a magnetic field of sufficient magnitude, provided the phase transition occurs during the final 5 e-foldings of the inflationary period.