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High thermoelectric performance in oxides requires stable conductive materials that have suitable band structures. Here we show, based on an analysis of the thermopower and related properties using first-principles calculations and Boltzmann transport theory in the relaxation time approximation, that hole-doped Cu _2 O may be such a material. We find that hole-doped Cu _2 O has a high thermopower of above 200  μ V K ^−1 even with doping levels as high as 5.2 × 10 ^20  cm ^−3 at 500 K, mainly attributed to the heavy valence bands of Cu _2 O. This is reminiscent of the cobaltate family of high-performance oxide thermoelectrics and implies that hole-doped Cu _2 O could be an excellent thermoelectric material if suitably doped.