If new physics (e.g. SUSY) does not show up as direct evidence at the LHC, it could still be observable in FCNC processes involving the t-quark. We take a close look at the process t -> c + h and show that its branching ratio in the Standard Model is subject to three mechanisms of suppression. To obtain an observable signal, one needs to evade all these mechanisms in a theory beyond the Standard Model. We show that a theory like the cMSSM cannot provide a big enough enhancement. However, in a framework like R-parity-violating SUSY, observable signals are a distinct possibility.