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Heinrich events are characterized by worldwide climate modifications. Over the Altiplano endorheic basin (high tropical Andes), the second half of Heinrich Stadial 1 (HS1a) was coeval with the highstand of the giant paleolake Tauca. However, the atmospheric mechanisms underlying this wet event are still unknown at the regional to global scale. We use cosmic-ray exposure ages of glacial landforms to reconstruct the spatial variability in the equilibrium line altitude of the HS1a Altiplano glaciers. By combining glacier and lake modeling, we reconstruct a precipitation map for the HS1a period. Our results show that paleoprecipitation mainly increased along the Eastern Cordillera, whereas the southwestern region of the basin remained relatively dry. This pattern indicates a southward expansion of the easterlies, which is interpreted as being a consequence of a southward shift of the Bolivian High. The results provide a new understanding of atmospheric teleconnections during HS1 and of rainfall redistribution in a changing climate.