The time at which the signal of climate change emerges from the noise of natural climate variability (Time of Emergence, ToE) is a key variable for climate predictions and risk assessments. Here we present a methodology for estimating ToE for individual climate models, and use it to make maps of ToE for surface air temperature (SAT) based on the CMIP3 global climate models. Consistent with previous studies we show that the median ToE occurs several decades sooner in low latitudes, particularly in boreal summer, than in mid-latitudes. We also show that the median ToE in the Arctic occurs sooner in boreal winter than in boreal summer. A key new aspect of our study is that we quantify the uncertainty in ToE that arises not only from inter-model differences in the magnitude of the climate change signal, but also from large differences in the simulation of natural climate variability. The uncertainty in ToE is at least 30 years in the regions examined, and as much as 60 years in some regions. Alternative emissions scenarios lead to changes in both the median ToE (by a decade or more) and its uncertainty. The SRES B1 scenario is associated with a very large uncertainty in ToE in some regions. Our findings have important implications for climate modelling and climate policy which we discuss.