Understanding the stability of the early Antarctic ice cap in the geological past is of societal interest because present-day atmospheric CO2 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 (δ18O) 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 CO2 levels on astronomical time scales that is not yet captured in existing proxy reconstructions.