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We introduce a notion of `proChow group' of varieties, agreeing with thenotion of Chow group for complete varieties and covariantly functorial withrespect to arbitrary morphisms. We construct a natural transformation from thefunctor of constructible functions to the proChow functor, extendingMacPherson's natural transformation. We illustrate the result by providing veryshort proofs of (a generalization of) two well-known facts onChern-Schwartz-MacPherson classes: Kwiecinski's product formula, and theEhlers-Barthel-Brasselet-Fieseler computation of Chern-Schwartz-MacPhersonclasses of toric varieties.Comment: 6 pages; to appear in the CRA

Classes de Chern des variétés singulières, revisitées