We investigate the prospects for discovering a top quark decaying into one light Higgs boson along with a charm quark in top quark pair production at the CERN Large Hadron Collider (LHC). A general two Higgs doublet model is adopted to study the signature of flavor changing neutral Higgs decay $t to cphi^0$, %or $bar{t} to bar{c}phi^0$ where $phi^0$ could be CP-even ($H^0$) or CP-odd ($A^0$). The dominant physics background is evaluated with realistic acceptance cuts as well as tagging and mistagging efficiencies. For a reasonably large top-charm-Higgs coupling ($lambda_{tc}/lambda_{t} agt 0.09$), the abundance of signal events and the %that our acceptance cuts reduction in physics background allow us to establish a $5sigma$ signal for $M_phi sim 125$ GeV at the LHC with a center of mass energy ($sqrt{s}$) of 8 TeV and an integrated luminosity of 20 fb$^{-1}$. The discovery potential will be greatly enhanced with the full energy of $sqrt{s} = 14$ TeV.
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