If low-energy supersymmetry is realized in nature, and if the appropriate supersymmetric partner of the Higgs boson, h, has a mass mh ⪡ mZ, then there is a decay chain Z → zh, followed by z → hh, which can be a significant part of all Z decays, perhaps 0.1%–1%. Depending on what is the lightest supersymmetric partner, the signature will be Z → h + missing momentum, perhaps accompanied by one or two isolated hard γ's. Decays involving both the Higgs scalar h and the pseudoscalar A are discussed, as well as ways to distinguish between them.