The covariant chiral kinetic equation (CCKE) is derived from the four-dimensional Wigner function by an improved perturbative method under the static equilibrium conditions. The chiral kinetic equation in three dimensions can be obtained by integration over the time component of the four-momentum. There is freedom to add more terms to the CCKE allowed by conservation laws. In the derivation of the three-dimensional equation, there is also freedom to choose coefficients of some terms in dx0/dτ and dx/dτ τ is a parameter along the worldline, and (x0,x) denotes the time-space position of a particle whose three-momentum integrals are vanishing. So the three-dimensional chiral kinetic equation derived from the CCKE is not uniquely determined in the current approach. The key assumption of our approach is the perturbation in powers of space-time derivative and constant electromagnetic field strength tensor under the static equilibrium conditions. To go beyond the current approach and overcome these problems one needs a new way of building up the three-dimensional chiral kinetic equation from the CCKE or directly from covariant Wigner equations.