  We consider the dynamics of p anti-D3 branes inside the Klebanov-Strassler
geometry, the deformed conifold with M units of RR 3-form flux around the S^3.
We find that for p<<M the system relaxes to a nonsupersymmetric NS 5-brane
``giant graviton'' configuration, which is classically stable, but quantum
mechanically can tunnel to a nearby supersymmetric vacuum with M-p D3 branes.
This decay mode is exponentially suppressed and proceeds via the nucleation of
an NS 5-brane bubble wall. We propose a dual field theory interpretation of the
decay as the transition between a nonsupersymmetric ``baryonic'' branch and a
supersymmetric ``mesonic'' branch of the corresponding SU(2M-p)x SU(M-p) low
energy gauge theory. The NS 5-brane tunneling process also provides a simple
explanation of the geometric transition by which D3-branes can dissolve into
3-form flux.
