The West Antarctic Ice Sheet Divide (WAIS Divide, WD) ice core is a newly drilled, high-accumulation deep ice core that provides Antarctic climate records of the past ~68 ka at unprecedented temporal resolution. The upper 2850 m (back to 31.2 ka BP) have been dated using annual-layer counting. Here we present a chronology for the deep part of the core (67.8-31.2 ka BP), which is based on stratigraphic matching to annual-layer-counted Greenland ice cores using globally well-mixed atmospheric methane. We calculate the WD gas age-ice age difference (Δage) using a combination of firn densification modeling, ice-flow modeling, and a data set of δ15N-N2, a proxy for past firn column thickness. The largest Δage at WD occurs during the Last Glacial Maximum, and is 525 ± 120 years. Internally consistent solutions can be found only when assuming little to no influence of impurity content on densification rates, contrary to a recently proposed hypothesis. We synchronize the WD chronology to a linearly scaled version of the layer-counted Greenland Ice Core Chronology (GICC05), which brings the age of Dansgaard-Oeschger (DO) events into agreement with the U/Th absolutely dated Hulu Cave speleothem record. The small Δage at WD provides valuable opportunities to investigate the timing of atmospheric greenhouse gas variations relative to Antarctic climate, as well as the interhemispheric phasing of the "bipolar seesaw".