We compute the one-loop helicity amplitudes for low-energy $νγ\toνγ$ scattering and its crossed channels in the standard model with massless neutrinos. In the center of mass, with $\sqrt{s} = 2ω\ll 2m_e$, the cross sections for these $2\to 2$ channels grow roughly as $ω^6$. The scattered photons in the elastic channel are circularly polarized and the net value of the polarization is non-zero. We also present a discussion of the optical activity of a sea of neutrinos and estimate the values of its index of refraction and rotary power.

9 pages, ReVTeX4, 6 figures included