A novel hybrid concentrating solar power/concentrating photovoltaic (CSP/CPV) collector is designed, simulated, and optimized for the purpose of power generation. The two-stage concentrator combines a primary parabolic trough with a secondary compound parabolic concentrator (CPC). Single junction Indium Gallium Phosphide (InGaP) and dual junction (InGaP)/Gallium Arsenide (GaAs) solar cells are examined as spectrally reflective beam splitting solar cells. The secondary CPC profile is optimized to guarantee geometric efficiency despite a non-continuous (i.e. segmented) profile and the final two-stage design achieves a geometric concentration ratio of 50 x on the thermal absorber. Optical, thermal, and cell performance models are used to determine net electric production for different configurations of the hybrid collector and combined with cost estimates to calculate $/W-exergy and $/W-electric. The down-selected design incorporates dual junction InGaP/GaAs cells, achieves 40% solar-to-exergy efficiency and 23% solar-to electric-efficiency at 600 degrees C, with a thermal fraction of 73% and installs for an estimated $2.15/W-electric.