SIMPLE energy-balance climate models of the Budyko/Sellers type1,2 predict that a small (2-5%) decrease in solar output could result in runaway glaciation on the Earth. But solar fluxes 25-30% lower early in the Earth's history3,4 apparently did not lead to this result. One currently favoured explanation is that high partial pressures of carbon dioxide, caused by higher volcanic outgassing rates and/or slower rates of silicate weathering, created a large enough greenhouse effect to keep the planet warm5-7. This does not resolve the problem of climate stability, however, because as we argue here, the oceans can freeze much more quickly than CO2 can accumulate in the atmosphere. Had such a transient global glaciation occurred in the distant past when solar luminosity was low, it might have been irreversible because of the formation of highly reflective CO2 clouds, similar to those encountered in climate simulations of early Mars8. Our simulations of the early Earth, incorporating the possible formation of such clouds, suggest that the Earth might not be habitable today had it not been warm during the first part of its history.