  Low-mass stars, ~1-2 solar masses, near the Main Sequence are efficient at
producing He-3, which they mix into the convective envelope on the giant branch
and should distribute into the Galaxy by way of envelope loss. This process is
so efficient that it is difficult to reconcile the low observed cosmic
abundance of He-3 with the predictions of both stellar and Big Bang
nucleosynthesis. In this paper we find, by modeling a red giant with a fully
three-dimensional hydrodynamic code and a full nucleosynthetic network, that
mixing arises in the supposedly stable and radiative zone between the
hydrogen-burning shell and the base of the convective envelope. This mixing is
due to Rayleigh-Taylor instability within a zone just above the
hydrogen-burning shell, where a nuclear reaction lowers the mean molecular
weight slightly. Thus we are able to remove the threat that He-3 production in
low-mass stars poses to the Big Bang nucleosynthesis of He-3.
