  We perform a first lattice QCD simulation including two-flavor dynamical
fermion with a chiral chemical potential. Because the chiral chemical potential
gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD
matter by the Monte Carlo simulation. By applying an external magnetic field to
this system, we obtain a finite induced current along the magnetic field, which
corresponds to the chiral magnetic effect. The obtained induced current is
proportional to the magnetic field and to the chiral chemical potential, which
is consistent with an analytical prediction.
