The ultimate objective of climate change mitigation is to reduce the amount of anthropogenic greenhouse gas (GHG) emissions in order to achieve “stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system” (UNFCCC, Article 2). This statement raises a number of questions regarding (i) what “dangerous interference” means, (ii) what GHG concentration level may considered “safe”, and (iii) what emissions pathway should be taken towards stabilization. Here we present a novel approach to coupled climate-carbon cycle modelling which allows one to estimate the probability that any given level of greenhouse gas emissions will exceed specified global mean temperature thresholds for “dangerous anthropogenic interference”, taking into consideration uncertainties in climate sensitivity and the carbon cycle response to climate change. Results obtained within this framework can serve as a basis for selecting a greenhouse gas emissions level given a global mean temperature target and an overshoot probability that society is willing to accept. For instance, we show that in order to stabilize global mean temperature at 2°C above pre-industrial levels with a probability of at least 0.66, cumulative CO2-equivalent emissions after 2000 must not exceed a best estimate of about 640 PgC, independent of the path taken to stabilization.