In this paper, the handedness dependent electromagnetically induced transparency (EIT) in a chiral metamaterial and its sensitivity to the coupling conditions are presented. A chiral metamaterial, consisting of an array of coupled cut-wire resonators (CWRs) supporting the radiative resonance, exhibits strong chiral responses around 4 GHz when excited by circularly polarized (LCP and RCP) waves. Split ring resonators (SRRs) are designed to support non-radiative resonances at the same frequencies. Through appropriately introducing SRRs into the CWR array, transmission peaks are observed in the EIT chiral system at the frequencies correspond to the stopbands of the CWR chiral metamaterial for both RCP and LCP excitations. Particularly, transmission peaks of -2.3 dB and -1.3 dB are observed around 3.75 GHz and 4.10 GHz, respectively, for RCP and LCP waves, in contrast to the corresponding -13 dB and -9.2 dB handedness dependent transmission dips. The sensitivities of the proposed chiral EIT effect on coupling between SRRs and the CWRs are also studied.