  We present a string theory construction of a gravity dual of a spatially
modulated phase. In our earlier work, we showed that the Chern-Simons term in
the 5-dimensional Maxwell theory destabilizes the Reissner-Nordstrom black
holes in anti-de Sitter space if the Chern-Simons coupling is sufficiently
high. In this paper, we show that a similar instability is realized on the
worldvolume of 8-branes in the Sakai-Sugimoto model in the quark-gluon plasma
phase. We also construct and analyze a non-linear solution describing the
end-point of the transition. Our result suggests a new spatially modulated
phase in quark-gluon plasma when the baryon density is above 0.8 N_f fm^{-3} at
temperature 150 MeV.
