This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network, and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been recently developed by the authors, is tailored and applied for strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.