  We study the rare top-quark decay t->ch, where h is a generic Higgs boson, at
a linear collider. If kinematically accessible, all models contain this decay
at some level due to quark flavor mixing. Some models, such as Model III of the
two-Higgs doublet model, have a tree-level top-charm-Higgs coupling, and the
branching ratio is close to 0.5%. Others, such as the MSSM, have a coupling
induced at one-loop, and can have a branching ratio in the range of 10^{-5} -
5x10^{-4}. We find that a linear collider of root(s) = 500 GeV and a luminosity
of 500 fb^{-1} will begin to be sensitive to this range of the coupling.
