  We argue that the presence of a very strong magnetic field in the chirally
broken phase induces inhomogeneous expectation values, of a spiral nature along
the magnetic field axis, for the currents of charge and chirality, when there
is finite baryon density or an imbalance between left and right chiralities.
This "chiral magnetic spiral" is a gapless excitation transporting the currents
of (i) charge (at finite chirality), and (ii) chirality (at finite baryon
density) along the direction of the magnetic field. In both cases it also
induces in the transverse directions oscillating currents of charge and
chirality. In heavy ion collisions, the chiral magnetic spiral possibly
provides contributions both to the out-of-plane and the in-plane dynamical
charge fluctuations recently observed at RHIC.
