  It was previously shown within chiral perturbation theory that the ground
state of QCD in a sufficiently large magnetic field and at nonvanishing, but
not too large, baryon chemical potential is a so-called chiral soliton lattice.
The crucial ingredient of this observation was the chiral anomaly in the form
of a Wess-Zumino-Witten term, which couples the baryon chemical potential to
the magnetic field and the gradient of the neutral pion field. It was also
shown that the chiral soliton lattice becomes unstable towards charged pion
condensation at larger magnetic fields. We point out that this instability
bears a striking resemblance to the second critical magnetic field of a type-II
superconductor, however with the superconducting phase appearing upon
increasing the magnetic field. The resulting phase has a periodically varying
charged pion condensate that coexists with a neutral pion supercurrent. We
construct this phase analytically in the chiral limit and show that it is
energetically preferred. Just like an ordinary type-II superconductor, it
exhibits a hexagonal array of magnetic flux tubes, and, due to the chiral
anomaly, a spatially oscillating baryon number of the same crystalline
structure.
