  We have measured the magnetic susceptibilities of single crystals of
Cu_{1-x}Zn_xGeO_3 with extremely low Zn concentration (x) lower than
x=5x10^{-3} at very low temperatures to investigate the spin-Peierls and
antiferromagnetic transitions. The results show that the undoped CuGeO_3 has no
antiferromagnetic phase down to 12 mK and there exists an antiferromagnetic
long-range order with the easy axis along the $c$ axis for x down to
1.12(2)x10^{-3}. The minimum observed Neel temperature was 0.0285 K for
x=1.12(2)x10^{-3} sample. From the concentration dependence of the Neel
temperature it is concluded that there is no critical concentration for the
occurrence of the antiferromagnetic long-range order.
