Detailed analysis of a site near Cincinnati, Ohio, shows that 14C ages of samples in a single geologic unit can have a range of several thousand years and ages from different stratigraphic units can overlap. At the Sharonville site, four 14C samples from organic silt below glaciogenic deposits have an inverted chronologic sequence, suggesting contamination, but nevertheless they indicate the silt was deposited before 27,000 yr B.P. A stump cluster in growth position, wood fragments, and moss from the upper surface of the silt may differ by as much as 2300 14C yr. Five ages from the stump cluster constrain the timing of a glacier advance of the Laurentide ice sheet to its southern limit in the Cincinnati area at 19,670 ?? 68 yr B.P. Overlying glaciogenic sediments contain transported wood that may be as much as 3200 yr older than the advance. This range of ages points out that, for a given site, several age measurements are required to determine when a glacier advance occurred. Because the measured ages in this study span the entire interval suggested for a twofold sequence of advance, retreat, and readvance of the margin of the Miami sublobe, we suggest a single advance to its terminal position in the Cincinnati area as an alternate hypothesis for testing. ?? 1990.