The real and imaginary parts of the eigen complex wave vector in a stratified lossy chiral medium for the case of oblique incidence are derived by using the phase-matching condition. Due to the fact that the real and imaginary parts are nonparallel, the eigen wave propagating in the medium is inhomogeneous. Then the refraction angle of the eigen wave can be deduced via the real part of the wave vector. Finally the propagation matrix of the obliquely incident wave in a stratified lossy chiral medium is derived based on the boundary conditions and the field equations of eigen wave in each region. By using the proposed method, the reflection, transmission, and propagation characteristics of plane wave with arbitrary incident angle in a stratified chiral medium can be analyzed.