Is Geodetic Precession of Massive Neutrinos the solution to the Solar Neutrino Problem?

We examine a recent suggestion by Milburn that slightly massive electron neutrinos, produced left-handed at the core of the sun, suffer geodetic precession adequate to render them right-handed (and therefore sterile) in sufficient numbers to solve the solar neutrino problem. In that light, we perform a complete, general-relativistic calculation of the geodetic spin precession of an ultrarelativistic particle in the Schwartzschild metric. We conclude that the effect is negligible, in disagreement with Milburn's analysis.