This paper studies the design of a mid-scale maritime supply chain for distribution of liquefied natural gas (LNG) from overseas sourcing locations, via a storage located at the coast, before transporting the LNG on land to industrial customers. The case company has signed contracts with a number of initial customers and expect that there will be more customers and increased demand in the years to come. However, it is currently uncertain whether and when new contracts will be signed. To capture this uncertainty with regard to which and how many future customers there will be, which directly affects the demand, we propose a multi-stage stochastic programming model, which maximizes the expected profits of the supply chain. The model aims at aiding decisions concerning the import of LNG, investments in floating storage units and customer distribution systems, and it has been applied on a real case study for distributing LNG to customers in a Brazilian state. It is shown that explicitly considering uncertainty in the modeling of this problem is very important, with a Value of Stochastic Solution of 13.2%, and that there are significant economies of scale in this supply chain. Most importantly, the multi-stage stochastic programming model and the analysis presented in this paper provided valuable decision support and managerial insights for the case company in its process of setting up the LNG supply chain.