  We study the relativistic hydrodynamics with chiral anomaly and dynamical
electromagnetic fields, namely Chiral MagnetoHydroDynamics (CMHD). We formulate
CMHD as a low-energy effective theory based on a generalized derivative
expansion. We demonstrate that the modification of ordinary
MagnetoHydroDynamics (MHD) due to chiral anomaly can be obtained from the
second law of thermodynamics and is tied to chiral magnetic effect. We further
study the real-time properties of chiral fluid by solving linearized CMHD
equations. We discover a remarkable "transition" at an intermediate axial
chemical potential $\mu_{A}$ between a stable Chiral fluid at low $\mu_{A}$ and
an unstable Chiral fluid at large $\mu_{A}$. We summarize this transition in a
"phase diagram" in terms of $\mu_{A}$ and the angle of the wavevector relative
to the magnetic field. In the unstable regime, there are four collective modes
carrying both magnetic and fluid helicity, in contrary to MHD waves which are
unpolarized. The half of the helical modes grow exponentially in time,
indicating the instability, while the other half become dissipative.
