The electromagnetic properties of a structure that is both chiral and periodic are investigated using coupled-mode equations. The chirality is characterized by the constitutive relations D = εE + iXicB and H = iXicE+B/µ, where Xic is the chiral admittance. The periodicity is described by a sinusoidal perturbation of the permittivity, permeability and chiral admittance. The coupled-mode equations are derived from physical considerations. The coupled-mode equations are used to examine bandgap structure and reflected and transmitted fields. Chirality is observed predominantly in transmission while periodicity is present in both reflection and transmission.