  The LHC experiments have analyzed the 7 and 8 TeV LHC data in the main Higgs
production and decay modes. Current analyses only loosely constrain an
anomalous top-Higgs coupling in a direct way. In order to strongly constrain
this coupling, the Higgs-top associated production is reanalyzed. Thanks to the
strong destructive interference in the t-channel for standard model couplings,
this process can be very sensitive to both the magnitude and the sign of a
non-standard top-Higgs coupling. We project the sensitivity to anomalous
couplings to the integrated luminosity of 50 fb^{-1}, corresponding to the data
collected by the ATLAS and CMS experiments in 7 and 8 TeV collisions, as of
2012. We show that the combination of di-photon and multi-lepton signatures,
originating from different combinations of the top and Higgs decay modes, can
be a potential probe to constrain a large portion of the negative top-Higgs
coupling space presently allowed by the ATLAS and CMS global fits.
