Worldwide power resources that could be extracted from the steady-state operation of ocean thermal energy conversion (OTEC) plants are estimated using a simple model. This order-of magnitude analysis indicates that about 3 X 109 kW (3 TW) may be available, at most. This value is much smaller than estimates currently suggested in the technical literature. It reflects the scale of the perturbation caused by massive OTEC seawater flow rates on the thermal structure of the ocean. Not surprisingly, maximum OTEC power nearly corresponds to deep cold seawater flow rates of the order of the average abyssal upwelling representative of the global thermohaline circulation.