The UN Framework Convention on Climate Change calls for "stabilization of greenhouse gas concentrations at a level that would prevent dangerous anthropogenic interference with the climate system." Even if we could determine a "safe" level of interference in the climate system, the sensitivity of global mean temperature to increasing atmospheric CO2 is known perhaps only to a factor of three or less. Here we show how a factor of three uncertainty in climate sensitivity introduces even greater uncertainty in allowable increases in atmospheric CO2 concentration and allowable CO2 emissions. Nevertheless, unless climate sensitivity is low and acceptable amounts of climate change are high, climate stabilization will require a massive transition to CO2 emission-free energy technologies.