We investigate the effect of a magnetic field on the vacuum of low-temperature QCD at large-N_c in the presence of a chiral chemical potential, using the holographic Sakai-Sugimoto model. Above some critical chemical potential we find an instability, which triggers a decay of the homogeneous vacuum to a non-homogeneous configuration with a spiral form, which we construct explicitly. We find that this decay is suppressed for sufficiently large magnetic field, and determine the critical strength. We find that the new vacuum does not exhibit the chiral magnetic effect. This is related to the way the chiral chemical potential is introduced. We discuss an alternative way of introducing the chiral chemical potential that leads to a nonzero chiral magnetic effect. ; Comment: 40 pages; v2: references added, minor typos corrected