The resonant splitting of optical Tamm state numerically is demonstrated. The Tamm state is localized at the interface between a resonant chiral medium and a polarization-preserving anisotropic mirror. The chiral medium is considered as a cholesteric liquid crystal doped with resonant dye molecules. The article shows that the splitting occurs when dye resonance frequency coincides with the frequency of the Tamm state. In this case the reflectance, transmittance, and absorptance spectra show two distinct Tamm modes. For both modes, the field localization is at the interface between the media. The external field control of configurable optical and structural parameters paves the way for use in tunable chiral microlaser.