High-temperature proton-exchange membrane fuel cells are a promising technology for distributed power generation thanks to their high-power density, high efficiency, low emissions, fast start-up, and excellent dynamic characteristics, together with their high tolerance to CO poisoning (i.e., CO in the feed up to 3%). In this paper, we present an innovative, simple, and efficient hybrid high-temperature proton-exchange membrane fuel cell gas turbine combined heat and power system whose fuel processor relies on partial oxidation. Moreover, we demonstrate that the state-of-the-art fuel processors based on steam reformation may not be the optimal choice for high-temperature proton-exchange membrane fuel cells’ power plants. Through steady-state modeling, we determine the optimal operating conditions and the performance of the proposed innovative power plant. The results show that the proposed hybrid combined heat and power system achieves an electrical efficiency close to 50% and total efficiency of over 85%, while a state-of-the-art system based on steam reformation has an electrical efficiency lower than 45%. The proposed innovative plant consists of a regenerative scheme with a limited power ratio between the turbine and fuel cell and limited optimal compression ratio. Therefore, micro-gas turbines are the most fitting type of turbomachinery for the hybrid system.