Recently, kinetic theory of chiral fermions has been developed. Spin of chiral fermions introduces an interesting nontrivial structure in the phase space: Berry connection in the momentum space in the monopole configuration. This new kinetic theory can describe the axial U(1) anomaly and the so-called chiral magnetic effect. In this talk, we consider QED and QCD plasmas with massless fermions and apply the new kinetic theory to the dynamics of gauge fields. When there is an imbalance between left-handed and right-handed fermions (chirality imbalance), we find that the gauge field becomes unstable. We call this instability chiral plasma instability. The unstable mode grows so as to reduce the chiral imbalance, which is the source of the instability. The effect of collisions is relevant for the instability of the QCD plasma while it is not for the QED plasma. We also develop an effective chiral Langevin theory for non-Abelian gauge fields in QCD plasma that describes both the chiral plasma instability and soft collisions.