The decay B-d --> phiK(S) is a special probe of physics beyond the standard model (SM), since it has no SM tree level contribution. Motivated by recent data suggesting a deviation from the SM for its time-dependent CP asymmetry, we examine supersymmetric explanations. Chirality preserving contributions are generically small, unless gluino is relatively light. Higgs contributions are also too small to explain a large asymmetry. Chirality flipping LR and RL gluino contributions actually can provide sizable effects without conflict with all related results. We discuss how various insertions can be distinguished, and argue the needed sizes of mass insertions are reasonable.