Uncertainty introduces significant complexity to the design process of distributed energy systems (DES) and introduces the risk of suboptimal decisions when the design is performed deterministically. Therefore, it is important that computational DES design models are able to account for the most relevant uncertainty sources when identifying optimal DES configurations. In this paper, a model for optimal DES design under uncertainty is presented and is formulated as a Two-stage Stochastic Mixed-Integer Linear Program. As uncertain parameters, energy carrier prices and emission factors, building heating and electricity demands, and incoming solar radiation patterns are considered and probabilistic scenarios are used to describe their uncertainty. The model seeks to make cost-optimal DES design decisions (technology selection and sizing) before these uncertain parameters are known, while it also identifies the optimal operation of the selected DES configuration for multiple uncertain scenarios. Moreover, two strategies for emission reduction are employed that set CO2 limits either to the system's average emissions under uncertainty ('neutral' strategy) or individually to the system's emissions for every possible uncertainty outcome to ensure a more robust emission performance ('aggressive' strategy). To illustrate the model's application, the design of a DES for a Swiss urban neighbourhood of 10 buildings is investigated. Multiple optimal DES configurations are obtained by using the 'neutral' and 'aggressive' emission reduction strategies and the trade-offs between the systems' economic and emission performance are analysed. Moreover, the optimal DES are contrasted in terms of technology selection and energy consumption shares among fossil fuels, grid electricity and renewable energy. Finally, all model outputs are compared to results obtained from a deterministic design model. The comparison showed that the deterministic model leads to underestimations of the system costs and inaccurate estimates of the system's CO2 emissions. Moreover, the deterministic designs, in many cases, underestimate the renewable energy capacity that is required to meet the imposed CO2 limits. These significant differences between the stochastic and the deterministic model results can serve to confirm the shortfalls of deterministic design.