  We investigate polarized gravitational waves generated by chiral fermions in
the early Universe. In particular, we focus on the contribution from
left-handed neutrinos in thermal equilibrium with finite temperature and
chemical potential in the radiation dominated era. We compute the correlation
functions of gravitational fields pertinent to the Stokes parameter $V$
characterizing the circular polarization of gravitational waves in the
Minkowski and expanding spacetime backgrounds. In the expanding universe, we
find that the thermalized neutrinos induce a non-vanishing $V$ linear to the
neutrino degeneracy parameter and wavenumber of gravitational waves in the long
wavelength region. While the magnitude of the gravitational waves generated by
thermal neutrinos is too small to be detectable by current and planned third
generation gravitational wave detectors, their observations by future
generation detectors for ultra-high frequency regimes could provide information
on the neutrino degeneracy parameter in the early Universe.
