  We present a scenario for efficient magnetization of very young galaxies
about 0.5 Gigayears after the Big-Bang by a cosmic ray-driven dynamo. These
objects experience a phase of strong star formation during this first $10^9$
years. We transfer the knowledge of the connection between star formation and
the production rate of cosmic rays by supernova remnants to such high redshift
objects. Since the supernova rate is a direct measure for the production rate
of cosmic rays we conclude that very young galaxies must be strong sources of
cosmic rays. The key argument of our model is the finding that magnetic fields
and cosmic rays are dynamically coupled, i.e. a strong cosmic ray source
contains strong magnetic fields since the relativistic particles drive an
efficient dynamo in a galaxy via their buoyancy. We construct a
phenomenological model of a dynamo driven by buoyancy of cosmic rays and show
that if azimuthal shearing is strong enough the dynamo amplification timescale
is close to the buoyancy timescale of the order of several $10^7 \div 10^8$ yr.
We predict that young galaxies are strongly magnetized and may contribute
significantly to the gamma-ray-background.
