Generation Capacity Expansion Planning (GCEP) decides about generation capacity investments to adequately supply the future loads, while minimizing investment and operation costs satisfying a set of technical and security constraints. This paper presents a Stochastic Mixed-Integer Programming formulation (SMIP) for suggesting future generation investments considering demand uncertainty. The method was applied to the Chilean Northern Interconnected System (SING) with a planning horizon of 14 years considering uncertainty on the possible future connection of large industrial and mining loads. The computational challenges posed by GCEP under uncertainty required compromising between the detail of the stochastic demand representation and the detail of the transmission system. Thus, scenario-reduction was applied to keep the problem of a manageable size without losing too much transmission detail. Our results for the SING showed that use of SMIP can bring expected savings of about 1.1% on the total investment plus expected operational cost with respect to optimization using an average demand scenario. Furthermore, the stochastic plan showed less variability across scenarios and proved to be more resilient to changes in the modeling assumptions than the other plans.