The expected increase in energy demand in the United States has led to the pursuit of more efficient methods to generate thermal and electrical energy for the residential sector. One possible approach that could both increase generation efficiency and reduce CO2 emissions is Combined Heat and Power (CHP). CHP plants, powered by natural gas, can act as an integrated residential utility supplier by producing the thermal and electrical energy needed to meet the heating, cooling, and electricity demands of a (future) residential neighborhood. However, a CHP plant operating in island (i.e., grid-disconnected) mode must be optimally sized to maximize efficiency and to lower the capital and marginal costs. In this paper, we describe a novel simultaneous optimization of design and operating strategies for a CHP plant as a utility producer for a residential neighborhood. The plant, operating in island mode, integrates distributed residential photovoltaic solar power generation, and is optimized to meet a time-dependent energy demand profile characteristic of residential energy use. To accurately capture the variability (hourly and seasonal) and uncertainty in residential energy demand and rooftop photovoltaic generation, a vast amount of energy data were incorporated in the problem formulation. The multi-scale optimization problem was solved using a temporal Lagrangean decomposition method, generating the design of a CHP plant that can efficiently meet all residential utility demands, taking into consideration the long-term (design) and short-term (operational) costs.