Combined heat and power systems aka CHP, may be optimally combined with a ground-source heat pump, provided that a careful energy and exergy analysis is made. In this case part of the generated power by the CHP unit drives the heat pump. In terms of the overall energy efficiency the ratio of the power allocated to the heat pump to the total power generated by the CHP system must be optimized. An earlier study of the same author based on energy efficiency alone showed that there is indeed an optimum solution for given design conditions, for maximum energy efficiency. However, this paper shows that it may not be the case if a thorough exergy analysis is carried out. New results indicate that when the quality of energy used is compared with the overall quality of supply energy derived from the CHP and the heat pump couple is compared, the results are not favorable for such a coupling unless the COP of the heat pump is very high. This paper covers a case study, namely the new ESER Office Building in Ankara, which received the first Platinum LEED Green Building Certificate in February 2011.