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We propose in this paper a novel integration of local search algorithms within a constraint programming framework for combinatorial optimization problems, in an attempt to gain both the efficiency of local search methods and the flexibility of constraint programming while maintaining a clear separation between the constraints of the problem and the actual search procedure. Each neighborhood exploration is performed by branch-and-bound search, whose potential pruning capabilities open the door to more elaborate local moves, which could lead to even better approximate results. Two illustrations of this framework are provided, including computational results for the traveling salesman problem with time windows. These results indicate that it is one order of magnitude faster than the customary constraint programming approach to local search and that it is competitive with a specialized local search algorithm.