An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) for the case of an active defect layer is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, an isotropic absorbing or amplifying 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. The dispersion equation determining connection of the defect mode frequency with the isotropic layer gain and thickness is obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-active defect layer-CLC) are presented and analyzed for absorbing and amplifying defect layers. The effect of anomalously strong light absorption at the defect mode frequency for absorbing defect layer is discussed. It is shown that in DFB lasing in a defect structure with an amplifying defect layer an adjusting of the lasing frequency to the DM frequency results in a significant lowering of the lasing threshold and the threshold gain is lowering with increase of defect layer thickness. Numerical estimates of the threshold gain are performed for typical values of the related parameters and analytic expressions for thick CLC layers in the defect structure are presented.