Expert elicitation studies have become important barometers of scientific knowledge about future climate change (Morgan and Keith, Environ Sci Technol 29(10), 1995; Reilly et al., Science 293(5529):430–433, 2001; Morgan et al., Climate Change 75(1–2):195–214, 2006; Zickfeld et al., Climatic Change 82(3–4):235–265, 2007, Proc Natl Acad Sci 2010; Kriegler et al., Proc Natl Acad Sci 106(13):5041–5046, 2009). Elicitations incorporate experts’ understanding of known flaws in climate models, thus potentially providing a more comprehensive picture of uncertainty than model-driven methods. The goal of standard elicitation procedures is to determine experts’ subjective probabilities for the values of key climate variables. These methods assume that experts’ knowledge can be captured by subjective probabilities—however, foundational work in decision theory has demonstrated this need not be the case when their information is ambiguous (Ellsberg, Q J Econ 75(4):643–669, 1961). We show that existing elicitation studies may qualitatively understate the extent of experts’ uncertainty about climate change. We designed a choice experiment that allows us to empirically determine whether experts’ knowledge about climate sensitivity (the equilibrium surface warming that results from a doubling of atmospheric CO2 concentration) can be captured by subjective probabilities. Our results show that, even for this much studied and well understood quantity, a non-negligible proportion of climate scientists violate the choice axioms that must be satisfied for subjective probabilities to adequately describe their beliefs. Moreover, the cause of their violation of the axioms is the ambiguity in their knowledge. We expect these results to hold to a greater extent for less understood climate variables, calling into question the veracity of previous elicitations for these quantities. Our experimental design provides an instrument for detecting ambiguity, a valuable new source of information when linking climate science and climate policy which can help policy makers select decision tools appropriate to our true state of knowledge.