We use a recently-developed efficient probabilistic estimation technique to estimate the sensitivity of the Earth's temperature to a doubling of atmospheric carbon dioxide. The method is based on the ensemble Kalman filter which we apply to the CCSR/NIES/ FRCGC AGCM (the atmospheric component of MIROC 3.2) at T21L20 resolution coupled to a slab ocean. The method combines prior beliefs about the model, with observational data, to simultaneously estimate 25 model parameters in an efficient and objective manner. We perform a sensitivity analysis to investigate the effect of different assumptions regarding model error, since this is a necessarily subjective input which has not yet been well characterised. We attempt to validate the resulting ensembles against out-of-sample data by comparing their hindcasts of the Last Glacial Maximum (LGM) to paleoclimate proxy data, and demonstrate through this that our ensembles of simulations are probably biased towards too high a sensitivity. Within the framework of our single-model ensemble experiment, we show that climate sensitivity of much greater than 6°C is hard to reconcile with the paleoclimate record, and that of greater than 8°C seems virtually impossible. Our estimate for the most likely climate sensitivity is in the region of 4.5°C. Although these results are reasonably consistent with the most widely accepted estimates of climate sensitivity, they disagree with some recent research which has suggested a significant probability of sensitivities well in excess of these values. These results suggest that paleoclimatic evidence could provide a useful, albeit imprecise, constraint on ensemble forecasts of future climate change.