Set constraints are inclusion relations between expressions denoting sets of ground terms over a randed alphabet. They are the main ingredient in set-based program analysis[3,4,12,13,17,20,21,22,26]. In this paper we describe a constraint logic programming language CLP(SC) over set constraints in the style of Jaffar and Lassez[15]. The language subsumes ordinary logic programs over an IIerbrand domain. We give an efficient unification algorithm and operational, declarative, and fixpoint semantics. We show how the language can be applied in set-based program analysis by deriving explicitly the monadic approximation of the collecting semantics of IIeintze and Jaffar[12,13].