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 S3. 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) × SU(M-p) low energy gauge theory. The NS 5-brane tunneling process also provides a simple visualization of the geometric transition by which D3-branes can dissolve into 3-form flux. © SISSA/ISAS 2002.