The rare decay B-->phiK(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-->psiK(S). Motivated by recent data suggesting new physics in B-->phiK(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-->psiK(S), DeltaM(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.