  Using the one-loop helicity amplitudes for low-energy $\nu\gamma\to\nu\gamma$
and $\bar\nu\gamma\to\bar\nu\gamma$ scattering in the standard model with
massless neutrinos, we study the optical activity of a sea of neutrinos and
antineutrinos. In particular, we estimate the values of the index of refraction
and rotary power of this medium in the absence of dispersion.
