Past behavior of outlet glaciers draining the East Antarctic Ice Sheet (EAIS) remains unresolved prior to Marine Isotope Stage 2 (MIS2). Study of blue ice moraines provides a relatively untapped approach to understand former EAIS activity. We focus on a blue ice moraine near Mount Achernar in the central Transantarctic Mountains, at the edge of the polar plateau. The well-preserved moraine consists of quasi-continuous or hummocky sediment ridges that form on top of upward-flowing, sublimating ice along the margin of Law Glacier. 10Be, 26Al, and 3He cosmogenic nuclide ages on boulders from the ridges are coherent and in general are progressively older with distance from the relatively clean ice of the Law Glacier margin. Moraines closest to the Law Glacier margin postdate MIS2; farther away, they date to the last glacial cycle, and with more distance they are hundreds of thousands of years old. We conclude that cosmogenic dating of some blue ice moraines can provide age limits for changes at the heads of outlet glaciers that drain the central East Antarctic Ice Sheet, including prior to MIS2. Furthermore, the geomorphological, cosmogenic nuclide, and sedimentological evidence imply that the East Antarctic polar plateau adjacent to the central Transantarctic Mountains has been relatively stable for at least 200 k.y.