The long-term goal of the Intergovernmental Panel on Climate Change (IPCC) is the stabilization of carbon concentration in the atmosphere. In this paper, we impose a carbon target concentration on a partial equilibrium model of the global energy sector. Specifically, we ask whether nuclear power can provide carbon-free energy as fossil fuel resources become costly due to scarcity and externality costs. We find that nuclear power can reduce the cost of generating clean energy significantly and relatively quickly. However, beyond a few decades the role of nuclear power may be considerably reduced as uranium becomes scarce and renewables become economical. The cost of carbon when nuclear power supplies a significant share of energy is much lower than that of other studies. A policy implication is that current political and regulatory impediments to the expansion of nuclear generation may prove to be costly if large volumes of clean energy need to be supplied over a relatively short period of time.