We show a possibility that there exists a color ferromagnetic state in quark matter, in which a color magnetic field is spontaneously generated. The state arises between the hadronic state and the color superconducting state when the density of quarks is varied.Although the state (Savvidy state) has been known to involve unstablemodes of gluons, we show that the modes compose a quantum Hall state to stabilize the ferromagnetic state. Such a quantum Hall statecan arise only when quarks matter is present. We also show that the order of the phase transition between the state andthe quark gluon plasma is of the first order.

9 pages