  Using the information on the nuclear structure of exotic neutron-rich halo
nucleus $^{11}$Be, we evaluate the parity violating anapole moment in its
ground state. The resulting value $\kappa(^{11}$Be)$=0.17$ is fifteen times
bigger than the typical value of the anapole moment of a normal nucleus of the
same mass, and in fact exceeds by few times anapole moments of any known
neutron-odd nuclei (e.g., kappa(^{11}Be) > 2|\kappa(^{207}Pb)|. It is also few
times bigger than the neutral current contribution to the lepton-nucleus
interaction.
