The characteristics of a slot antenna on a perfectly conducting elliptic cylinder coated by nonconfocal chiral media are investigated. The structure is fed with a line source or plane wave. The analysis is carried out by expressing the fields in and around the cylinder in terms of Mathieu and modified Mathieu functions using the separation of variable and exact boundary value technique. The unknown aperture field is expressed in terms of Fourier series with unknown expansion coefficients. The expansion coefficients are found by applying the boundary conditions on different surfaces and employing the addition theorem and orthogonality properties of the Mathieu functions. For TM and TE cases some numerical results of the antenna gain for co-and cross-polarized waves are presented and discussed.