  We present radiometric $^{81}$Kr dating results for ice samples collected at
the outlets of the Guliya ice cap in the western Kunlun Mountains of the
Tibetan Plateau. This first application of $^{81}$Kr dating on mid-latitude
glacier ice was made possible by recent advances in Atom Trap Trace Analysis,
particularly a reduction in the required sample size down to 1 $\mu$L STP of
krypton. Eight ice blocks were sampled from the bottom of the glacier at three
different sites along the southern edges. The $^{81}$Kr data yield upper age
limits in the range of 15-74 ka (90% confidence level). This is an order of
magnitude lower than the ages exceeding 500 ka which the previous $^{36}$Cl
data suggest for the bottom of the Guliya ice core. It is also significantly
lower than the widely used chronology up to 110 ka established for the upper
part of the core based on $\delta^{18}$O in the ice.
