Stratospheric sulfate aerosols from explosive volcanic eruptions reflect incoming solar radiation and cool the planet, leading to the hypothesis that the largest volcanic events triggered millennial-scale cold periods over the last ice age. Here, we identify tephra shards from the Atitlán Los Chocoyos supereruption (LCY), one of the largest Quaternary eruptions, in ice cores from Greenland and Antarctica (dated at 79.5 ± 1.7 ka), and a marine sediment core (linked to a sea level highstand at 80.5 ± 0.9 ka). The large ice core sulfate peak associated with the tephra results in an estimated stratospheric sulfur injection of 226 ± 48 Tg S (1σ) for LCY, consistent with volcanic-induced cooling on a multi-annual scale. However, the well-constrained timing of LCY within the high-resolution temperature proxy records of ice cores proves it was not a trigger of millennial-scale cooling.