  We revisit the evaluation of the chiral vortical effect in the accelerated
matter. To first order in the acceleration the corresponding matrix element of
the axial current can be reconstructed from the flat-space limit. A crucial
point is the existence in the this case of an extra conservation law of fluid
helicity. As a result, the chirality of the microscopic degrees of freedom and
helicity of the macroscopic motion are separately conserved. This separation
persists also in presence of gravity. Implications for the thermal chiral
vortical effect are discussed.
