An interesting feature of the next-to-minimal supersymmetric standard model (NMSSM) is that one or more Higgs bosons may be comparably light (M_{H_i}<M_Z) without being in conflict with current experimental bounds. Due to a large singlet component, their direct production in standard channels at the Large Hadron Collider (LHC) is suppressed. We demonstrate that there are good prospects for observing such a light Higgs boson in decays of heavy neutralinos and charginos. We consider an example scenario with 20 GeV < M_{H_1} < M_Z and show that a large fraction of the cascade decays of gluinos and squarks involves the production of at least one Higgs boson. Performing a Monte Carlo analysis at the level of fast detector simulation, it is demonstrated how the Higgs signal can be separated from the main backgrounds, giving access to the Yukawa coupling of the Higgs to bottom quarks. Analyzing the resulting b\bar{b} mass spectrum could provide an opportunity for light Higgs boson discovery already with 5 fb^{-1} of LHC data at 7 TeV.