  Within gauge/gravity duality, we study the class of four dimensional CFTs
with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five
dimensions. In particular we determine the phase diagram at finite temperature,
chemical potential and magnetic field. At high temperatures the solution is
given by an electrically and magnetically charged AdS Reissner-Nordstroem black
brane. For sufficiently large Chern-Simons coupling and at sufficiently low
temperatures and small magnetic fields, we find a new phase with helical order,
breaking translational invariance spontaneously. For the Chern-Simons couplings
studied, the phase transition is second order with mean field exponents. Since
the entropy density vanishes in the limit of zero temperature we are confident
that this is the true ground state which is the holographic version of a chiral
magnetic spiral.
