pro-Chow groups and Chern-Schwartz-MacPherson classes

I will recall a conjecture of Grothendieck and Deligne, solved by MacPherson in the early '70s. I will describe a new proof of this conjecture, based on the introduction of a functor extending the functoriality of Chow groups to non-proper maps. The corresponding new construction of "Chern-Schwartz-MacPherson classes" is in some ways simpler than the original construction by MacPherson, and yields very short proofs of some known facts about these classes.