  Microgauss magnetic fields are observed in all galaxies at low and high
redshifts. The origin of these intense magnetic fields is a challenging
question in astrophysics. We show here that the natural plasma fluctuations in
the primordial universe (assumed to be random), predicted by the
Fluctuation-Dissipation-Theorem, predicts $\sim 0.034 \mu G$ fields over $\sim
0.3$ kpc regions in galaxies.
  If the dipole magnetic fields predicted by the
Fluctuation-Dissipation-Theorem are not completely random, microgauss fields
over regions $\gtrsim 0.34$ kpc are easily obtained. The model is thus a strong
candidate for resolving the problem of the origin of magnetic fields in
$\lesssim 10^{9}$ years in high redshift galaxies.
