After the discovery of a 126 GeV state at the LHC, it is imperative to establish whether this particle really is the Higgs boson of the standard model. The early measurements have not yet pinpointed any of the Higgs couplings to fermions, the Yukawa couplings of the standard model. In this paper we study the values of the top-quark-Higgs coupling, ghtt̄, that are still allowed by the one-loop couplings of the Higgs to two gluons or two photons. We first assume that both the gluon fusion production of the Higgs and its decay into two photons proceed through loops with standard model particles only, albeit with an arbitrary top-Higgs coupling. We find that the current Higgs data still allow for 20% deviations in ghtt̄ from its standard model value. We then investigate the effect of new particles contributing to the effective one-loop couplings. Specifically, we consider a color-octet electroweak doublet extension of the scalar sector and find that, in this case, ghtt̄ is allowed to deviate from its standard model value by 40% with the current data.