  Low-mass stars, ~1-2 solar masses, near the Main Sequence are efficient at
producing 3He, which they mix into the convective envelope on the giant branch
and distribute into the Galaxy by way of envelope loss. This process is so
efficient that it is difficult to reconcile the observed cosmic abundance of
3He with the predictions of 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. In this zone the burning of the 3He
left behind by the retreating convective envelope is predominantly by the
reaction 3He + 3He -> 4He + 2p, a reaction which, untypically for stellar
nuclear reactions, {\it lowers} the mean molecular weight, leading to a local
minimum. This local minimum leads to Rayleigh-Taylor instability, and turbulent
motion is generated which will continue ultimately up into the normal
convective envelope. Consequently material from the envelope is dragged down
sufficiently close to the burning shell that the 3He in it is progressively
destroyed. Thus we are able to remove the threat that 3He production in
low-mass stars poses to the Big Bang nucleosynthesis of 3He. Some slow mixing
mechanism has long been suspected, that connects the convective envelope of a
red giant to the burning shell. It appears to be necessary to account for
progressive changes in the 12C/13C and 14N/12C ratios on the First Giant
Branch. We suggest that these phenomena are also due to the
Rayleigh-Taylor-unstable character of the 3He-burning region.
