We investigate the propagation of electromagnetic waves in a one-dimensional photonic crystal containing a defect layer made of an isotropic chiral medium. Using the invariant imbedding method, we calculate the transmission spectrum for both linearly- and circularly-polarized incident waves. In the normal incidence case, there is one defect mode, which does not depend on the chiral index and the polarization of the incident wave. When the waves are incident obliquely, however, we find that there appear double defect modes regardless of the polarization. The interval between the two defect frequencies increases monotonically as the chiral index or the incident angle increases. We argue that this phenomenon occurs due to the coupling and conversion between s and p waves inside the chiral defect layer.