This paper presents the first systematic attempt to map the Last Glacial Maximum (LGM) configuration of the southern and central parts of the Antarctic Peninsula Ice Sheet, and to determine the timing of onshore ice-sheet retreat. Geomorphologic evidence shows that the LGM ice sheet expanded to form two ice domes in Palmer Land and merged with an expanded and thicker West Antarctic Ice Sheet in the Weddell Sea. Ice from the Antarctic Peninsula merged with Alexander Island ice in George VI Sound. Cosmogenic 10Be and 26Al data from 29 erratics on nunataks yield model ages between 7.2 ka and older than 1 Ma. The data set contains a high proportion of erratics with evidence of nuclide inheritance. Once these ages have been excluded, the cosmogenic ages suggest that thinning of the west side of the Antarctic Peninsula Ice Sheet to near-present configuration was almost complete by the early Holocene. These data, combined with previously published 14C data, exclude the possibility that the west side of the Antarctic Peninsula Ice Sheet has been thinning throughout the Holocene, as has been demonstrated for some other sectors of the West Antarctic Ice Sheet. On the east side of the Antarctic Peninsula, ice-sheet thinning was under way prior to the early Holocene, but our data do not constrain the ice-sheet behavior more recently than 7.2 ka.