  For a toric variety X_P determined by a rational polyhedral fan P in a
lattice N, Payne shows that the equivariant Chow cohomology of X_P is the
Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use
the Cartan-Eilenberg spectral sequence to analyze the associated reflexive
sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P
and giving criteria for the splitting of the sheaf as a sum of line bundles.
For certain fans associated to the reflection arrangement A_n, we describe a
connection between C^0(P) and logarithmic vector fields tangent to A_n.
