  We show that the evolution of magnetic fields in a primordial plasma, filled
with Standard Model particles, at temperatures T > 10 MeV is strongly affected
by the quantum chiral anomaly -- an effect that has been neglected previously.
Although reactions equilibrating left and right-chiral electrons are in deep
thermal equilibrium for T < 80 TeV, an asymmetry between these particle
develops in the presence of strong magnetic fields. This results in magnetic
helicity transfer from shorter to longer scales. This also leads to an
effective generation of lepton asymmetry that may survive in the plasma down to
temperatures T ~ 10 MeV, which may strongly affect many processes in the early
Universe. Although we report our results for the Standard Model, they are
likely to play an important role also in its extensions.
