  We study dispersion relations of hydrodynamic waves of hot N=4 SYM plasma at
strong coupling with a finite U(1) R-charge chemical potential via holography.
We first provide complete equations of motion of linearized fluctuations out of
a charged AdS black-hole background according to their helicity, and observe
that helicity +1 and -1 transverse shear modes receive a new parity-odd
contribution from the 5D Chern-Simons term, which is dual to 4D U(1)^3 anomaly.
We present a systematic solution of the helicity +1,-1 wave equations in long
wave-length expansion, and obtain the corresponding dispersion relations. The
results depend on the sign of helicity, which may be called chiral shear waves.
