Many exact or approximate solution techniques have been used to solve facility location problems and more generally supply chain network design problems. Yet, the Large Neighborhood Search technique (LNS) has almost never been proposed for solving such problems, although it has proven its efficiency and flexibility in solving other complex combinatorial optimization problems. In this paper we propose an LNS framework for solving a four-layer single period multi-product supply chain network design problem involving multimodal transport. Location decisions for intermediate facilities (e.g. plants and distribution centers) are made using the LNS while transportation modes and product flow decisions are determined by a greedy heuristic. As a post-optimization step, we also use linear programming to determine the optimal product flows once the logistics network is fixed. Extensive experiments based on generated instances of different sizes and characteristics show the effectiveness of the method compared with a state-of-the-art solver.