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Water resources in many of the world's arid mountain ranges are threatened by climate change, and in parts of the South American Andes this is exacerbated by glacier recession and population growth. Alternative sources of water, such as more resilient permafrost features (e.g. rock glaciers), are expected to become increasingly important as current warming continues. Assessments of current and future permafrost extent under climate change are not available for the Southern Hemisphere, yet are required to inform decision making over future water supply and climate change adaptation strategies. Here, downscaled model outputs were used to calculate the projected changes in permafrost extent for a first-order assessment of an example region, the Bolivian Andes. Using the 0 °C mean annual air temperature as a proxy for permafrost extent, these projections show that permafrost areas will shrink from present day extent by up to 95 % under warming projected for the 2050s and by 99 % for the 2080s (under the IPCC A1B scenario, given equilibrium conditions). Using active rock glaciers as a proxy for the lower limit of permafrost extent, we also estimate that projected temperature changes would drive a near total loss of currently active rock glaciers in this region by the end of the century. In conjunction with glacier recession, a loss of permafrost extent of this magnitude represents a water security problem for the latter part of the 21st century, and it is likely that this will have negative effects on one of South America's fastest growing cities (La Paz), with similar implications for other arid mountain regions.