We evaluate the LHC discovery potential for a light Higgs boson in t tbar H (-> l nu b bbar b bbar jj) production, within the Standard Model and if a new Q=2/3 quark singlet T with a moderate mass exists. In the latter case, T pair production with decays T Tbar -> W+ b H tbar / H t W- bbar -> W+ b W- bbar H provides an important additional source of Higgs bosons giving the same experimental signature, and other decay modes T Tbar -> H t H tbar -> W+ b W- bbar H H, T Tbar -> Z t H tbar / H t Z tbar -> W+ b W- bbar H Z further enhance this signal. Both analyses are carried out with particle-level simulations of signals and backgrounds, including t tbar plus n=0...5 jets which constitute the main background by far. Our estimate for SM Higgs discovery in t tbar H production, 0.4 sigma significance for M_H = 115 GeV and an integrated luminosity of 30 fb^-1, is similar to the most recent ones by CMS which also include the full t tbar nj background. We show that, if a quark singlet with a mass m_T = 500 GeV exists, the luminosity required for Higgs discovery in this final state is reduced by more than two orders of magnitude, and 5 sigma significance can be achieved already with 8 fb^-1. This new Higgs signal will not be seen unless we look for it: with this aim, a new specific final state reconstruction method is presented. Finally, we consider the sensitivity to search for Q=2/3 singlets. The combination of these three decay modes allows to discover a 500 GeV quark with 7 fb^-1 of luminosity.