  The neutrons cannot possess a quadrupole moment in the vacuum. Nevertheless,
we show that in the presence of an external magnetic field the neutrons acquire
a new type of quadrupole moment $Q^{ij}= \chi\,\sigma^i B^j$ involving the
components of spin and magnetic field. This "chiral magnetic" quadrupole moment
arises from the interplay of the chiral anomaly and the magnetic field; we
estimate its value for the neutron in the static limit, and find $\chi \simeq
1.35\cdot10^{-2}\,{\rm fm}^4$. The detection of the quadrupole moment of the
neutron would provide a novel test of the role of the chiral anomaly in
low-energy QCD and can be possible in the presence of both magnetic and
inhomogeneous electric fields. The quadrupole moment of the neutron may affect
e.g. the properties of neutron stars and magnetars.
