Despite increasing evidence that climatic changes are having a widespread effect on the global distribution and abundance of wildlife, the key question of whether the ranges of species that are already threat-listed are likely to be disproportionately affected lacks quantitative assessment. According to the "small-range climate-hypersensitivity hypothesis", we predict small range size to be directly linked to large climate-induced range reduction. Antelopes, an exemplary macroecological model due to their striking ecological diversity and species richness, present an ideal opportunity to test this. Here we provide the first empirical evidence that climate change will cause a disproportionate decline in African antelopes with small geographic ranges, which places the most threatened taxa in double jeopardy. This substantiates our theoretical expectation that the link between small range size and large climate induced range reduction is a general phenomenon. Our empirically based models also allow specific recommendations for mitigating climate-induced species declines. Gap analysis shows high priorities for antelope conservation to include creation of new protected areas in the horn of Africa and Liberia, as well as improved connectivity between existing protected areas. Predicted extinction of four species unable to reach areas with suitable climatic conditions by 2080 moreover highlights a potentially important role for ex situ conservation. The study emphasizes the urgent need to incorporate climate change into the IUCN threat assessment by extending the timeframe over which population trends are assessed.