Understanding the stability of the early Antarctic ice cap in the geological past is of societal interest because present-day atmospheric CO concentrations have reached values comparable to those estimated for the Oligocene and the Early Miocene epochs. Here we analyze a new high-resolution deep-sea oxygen isotope (δO) record from the South Atlantic Ocean spanning an interval between 30.1 My and 17.1 My ago. The record displays major oscillations in deep-sea temperature and Antarctic ice volume in response to the ∼110-ky eccentricity modulation of precession. Conservative minimum ice volume estimates show that waxing and waning of at least ∼85 to 110% of the volume of the present East Antarctic Ice Sheet is required to explain many of the ∼110-ky cycles. Antarctic ice sheets were typically largest during repeated glacial cycles of the mid-Oligocene (∼28.0 My to ∼26.3 My ago) and across the Oligocene-Miocene Transition (∼23.0 My ago). However, the high-amplitude glacial-interglacial cycles of the mid-Oligocene are highly symmetrical, indicating a more direct response to eccentricity modulation of precession than their Early Miocene counterparts, which are distinctly asymmetrical-indicative of prolonged ice buildup and delayed, but rapid, glacial terminations. We hypothesize that the long-term transition to a warmer climate state with sawtooth-shaped glacial cycles in the Early Miocene was brought about by subsidence and glacial erosion in West Antarctica during the Late Oligocene and/or a change in the variability of atmospheric CO levels on astronomical time scales that is not yet captured in existing proxy reconstructions.