An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, an isotropic layer (with the dielectric susceptibility equal to the average dielectric susceptibility of CLC) sandwiched between two CLC layers is studied. The chosen model allows one to get rid off the polarization mixing and to reduce the corresponding equations to the equations for light of diffracting in CLC polarization only. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-layer-CLC) are obtained as well as the dispersion equation determining connection of the defect mode frequency with the isotropic layer thickness. A limiting case of infinitely thick CLC-layers is considered in details. The developed approach helps to clarify the physics of the optical defect modes in CLC and manifests an excellent agreement with the corresponding results of the previous investigations obtained by a numerical approach.