  We study $T$-linear schemes, a class of objects that includes spherical and
Schubert varieties. We provide a localization theorem for the equivariant Chow
cohomology of these schemes that does not depend on resolution of
singularities. Furthermore, we give an explicit presentation of the equivariant
Chow cohomology of possibly singular complete spherical varieties admitting a
smooth equivariant envelope (e.g. group embeddings).
