Given a fleet of vehicles assigned to a single depot, the vehicle routing problem with time windows (VRPTW) consists of determining a set of feasible vehicle routes to deliver goods to a set of customers while minimizing, first, the number of vehicles used and, second, total distance traveled. A large number of heuristic approaches for the VRPTW have been proposed in the literature. In this paper, we present a large neighborhood search algorithm that takes advantage of the power of branch-and-price which is the leading methodology for the exact solution of the VRPTW. To ensure diversification during the search, this approach uses different procedures for defining the neighborhood explored at each iteration. Computational results on the Solomon's and the Gehring and Homberger's benchmark instances are reported. Compared to the best known methods, the proposed algorithm produces better solutions, especially on the largest instances where the number of vehicles used is significantly reduced.