We use localization to describe the restriction map from equivariant Chow cohomology to
ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial
functions and Minkowski weights. We compute examples showing that this map is not
surjective in general, and that its kernel is not always generated in degree one. We prove a
localization formula for mixed volumes of lattice polytopes and, more generally, a Bott
residue formula for toric vector bundles.