  We introduce a notion of `proChow group' of varieties, agreeing with the
notion of Chow group for complete varieties and covariantly functorial with
respect to arbitrary morphisms. We construct a natural transformation from the
functor of constructible functions to the proChow functor, extending
MacPherson's natural transformation. We illustrate the result by providing very
short proofs of (a generalization of) two well-known facts on
Chern-Schwartz-MacPherson classes: Kwiecinski's product formula, and the
Ehlers-Barthel-Brasselet-Fieseler computation of Chern-Schwartz-MacPherson
classes of toric varieties.
