The problem of EM wave propagation in non-reciprocal chiral media has been studied by several investigators. In a recent approach, a dual-transform technique has been developed to study the problem of such propagation under paraxial and slow-envelope variation conditions. In this paper, we first outline some of the results obtained using the dual transform technique for arbitrary boundary conditions within the left boundary of a semi-infinite, non-reciprocal chiral medium for a uniform plane wave, and a fundamental Gaussian-profiled beam. Next, we explore the problem of a uniform EM wave incident at an oblique angle at an interface between a reciprocal, non-chiral medium and a non-reciprocal, chiral medium. To carry out the calculations, the appropriate Maxwell's equations are examined together with the necessary boundary conditions, and reflection and transmission coefficients are derived for both parallel and perpendicular polarizations. The results are first tested for convergence in the reciprocal, non-chiral limit, and also for their physical implications under varying interfacial conditions.