The climate of the Last Glacial period (10,000 to 110,000 years ago) was characterized by rapid millennial-scale climate fluctuations termed Dansgaard/Oeschger (D/O) and Heinrich events. We present results from a speleothem-derived proxy of the South American summer monsoon (SASM) from 16,000 to 50,000 years ago that demonstrate the occurrence of D/O cycles and Heinrich events. This tropical Southern Hemisphere monsoon reconstruction illustrates an antiphase relationship to Northern Hemisphere monsoon intensity at the millennial scale. Our results also show an influence of Antarctic millennial-scale climate fluctuations on the SASM. This high-resolution, precisely dated, tropical precipitation record can be used to establish the timing of climate events in the high latitudes of the Northern and Southern Hemispheres.