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Zero Emission Neighborhoods (ZEN) is a concept studied in Norway to reduce the CO_2 emission of neighborhoods. One question coming along this concept is how to design the energy system of such neighborhoods to fit the ZEN definition. From this definition we extract the CO_2 balance, requiring an annual net zero emission of CO_2 in the lifetime of the neighborhood. This paper proposes a MILP model for obtaining cost optimal design of ZEN's energy system and demonstrates it on a case study. Different technologies are included as investment options and, notably PV as an on-site electricity production mean. Wind turbines are not included in this study because inappropriate in the context of most cities. The results for the case study highlight the importance of PV investment in reaching the ZEN requirements. For example, around 850 kW of solar is needed for our test cases of 10 000 m^2 of floor area, for an annual energy demand of around 700 MWh of electricity and 620 MWh of heat. The investments in other technologies are small in comparison.