The United Nations Framework Convention on Climate Change  calls for "stabilization of greenhouse-gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system...". A standard baseline scenario [2,3] that assumes no policy intervention to limit greenhouse-gas emissions has 10 TW (10 x 1012 watts) of carbon-emission-free power being produced by the year 2050, equivalent to the power provided by all today's energy sources combined. Here we employ a carbon-cycle/energy model to estimate the carbon-emission-free power needed for various atmospheric CO2 stabilization scenarios. We find that CO2 stabilization with continued economic growth will require innovative, cost-effective and carbon-emission-free technologies that can provide additional tens of terawatts of primary power in the coming decades, and certainly by the middle of the twenty-first century, even with sustained improvement in the economic productivity of primary energy. At progressively lower atmospheric CO2-stabilization targets in the 750-350 p.p.m.v. range, implementing stabilization will become even more challenging because of the increasing demand for carbon-emission-free power. The magnitude of the implied infrastructure transition suggests the need for massive investments in innovative energy research.