Continental sediments underlying the Altiplano plateau provide insight into the late Cenozoic evolution of the Central Andes. We characterize the magnetostratigraphy and lithostratigraphy of the upper part of this fill sequence along a transect extending southwestward from the Cordillera Real at La Paz, Bolivia, where it is best exposed. Multiple polarity reversals and the locally extensive, 2.74-Ma Chijini Tuff enable correlation between our six sections and three previously reported sections. The tuff ties the composite polarity sequence to the geomagnetic polarity time scale, demonstrating that the stratigraphic record extends from the latest Gilbert Chron (ca. 3.8 Ma) to the late Olduvai subchron (ca. 1.8 Ma), or possibly Jaramillo subchron (ca. 1.0 Ma). The sequence provides Earth's longest known record of low-latitude glaciation and the only record of Pliocene tropical glaciation. It includes evidence for 16 late Pliocene and Early Pleistocene glaciations, separated by interglacials of sufficient length (>103-104 a) to produce mature soil profiles. Successively larger ice caps formed directly before, during, and after the globally warm mid-Piacenzian (3.265–3.025 Ma), and throughout Plio-Pleistocene climate deterioration. The late Pliocene glacial units predate the onset of widespread Northern Hemisphere continental glaciation and in most cases unambiguously correspond to specific cool peaks of the astronomically tuned, benthic oxygen isotope (δ18O) record, including marine isotope stages MG2, M2, KM2, and G10. The glacial events broadly coincide with those nearer both poles, suggesting inter-hemispheric climate linkages. The early formation and subsequent expansion of ice caps beyond glacier margins of the Last Glacial Maximum suggest that the Cordillera Real likely attained its modern height before ca. 3.4 Ma. The number and timing of glaciations, and long-term sediment accumulation and incision rates suggest that the local Altiplano surface formed by ca. 1.8 Ma, after which headwaters of the Amazon River system breached the Cordillera Real and began to incise the fill sequence. The sequence spans at least 2 Ma before and during the first main pulses of the Great American Biotic Interchange, providing an important record of faunal migration. The arrival of savanna-adapted North American mammals in the Central Andes during this period points to the influence of glaciation on faunal migration in the southern tropics, similar to influences proposed in North and Central America.