In the paper the well known ray method is generalized to the case of the inhomogeneous chiral electromagnetic media. The electromagnetic field decompose in a chiral medium into two components with different propagation velocities. In the paper each of these components are presented in the form of ray expantions. The coefficients of these expantions are calculated in the ray coordinates which are attributed to the characteristics of eikonal equations. The leading and admixed components of the electromagnetic vectors are investigated and the polarization effects for both field components are analysed.