  The rare decay B --> Phi K_S is a well-known probe of physics beyond the
Standard Model because it arises only through loop effects yet has the same
time-dependent CP asymmetry as B --> Psi K_S. Motivated by recent data
suggesting new physics in B --> Phi K_S, we look to supersymmetry for possible
explanations, including contributions mediated by gluino loops and by Higgs
bosons. Chirality-preserving LL and RR gluino contributions are generically
small, unless gluinos and squarks masses are close to the current lower bounds.
Higgs contributions are also too small to explain a large asymmetry if we
impose the current upper limit on B(B_s --> mu mu). On the other hand,
chirality-flipping LR and RL gluino contributions can provide sizable effects
and while remaining consistent with related results in B --> Psi K_S, Delta
M_s, B --> X_s gamma and other processes. We discuss how the LR and RL
insertions can be distinguished using other observables, and we provide a
string-based model and other estimates to show that the needed sizes of mass
insertions are reasonable.
