  Starting from the data of a nonsingular complex projective toric variety, we
define an associated notion of toric co-Higgs bundle. We provide a
Lie-theoretic classification of these objects by studying the interaction
between Klyachko's fan filtration and the fiber of the co-Higgs bundle at a
closed point in the open orbit of the torus action. This can be interpreted,
under certain conditions, as the construction of a coarse moduli scheme of
toric co-Higgs bundles of any rank and with any total equivariant Chern class.
