Tephra-banded ice samples from the main Allan Hills icefield, Antarctica, are dated by a uranium-series method, which is based on the ^Ra/^Th and ^Ra/^U ratios dissolved in ice from tephra. The consistence between the age determined from the ^Ra/^Th ratio with the age determined from the ^Ra/^U ratio serves as a check on the method. For ice from a location at the western border of the 50-km^2 area that is richly laden with meteorites, the ^Ra/^Th and ^Ra/^U ages are (95±10)×10^3 and (100±10)×10^3 years, respectively. For ice from a location within this meteorite-rich area near its eastern border (approximately 5km closer to the Allan Hills land barrier), these ages are (185±25)×10^3 and (210±30)×10^3 years, respectively. The ice flow is from west to east, the dates indicate that most of the ice in the meteorite-rich area is between 1×10^5 and 2×10^5 years old with the age of the ice increasing in the flow direction as theoretically predicted for ice approaching a land barrier. The comparison of this ice chronology with the terrestrial ages of the meteorites leads to a number of conclusions about the meteorite fall rate and history of the ice movement