The potential applications of electromagnetic (EM) chirality, together with the fact that a general ellipsoid shape can simulate a variety of common objects, such as discs, needles etc., constitute the motivation of the present work. Scattering of EM waves incident on an ellipsoidal object of chiral property is analyzed using Fourier analysis, in conjunction with an integral equation technique. The inner field of the scatterer is described in terms of superposition of plane waves satisfying the vector Helmholtz wave equation inside the chiral media and a Galerkin procedure is employed to solve a volume integral equation obtained by applying the Green's theorem. A highly stable numerical code is obtained, which is verified by comparison with previously published solutions. Numerical computations have been carried out for various scatterers and interesting scattering properties of waves from chiral media are observed. Especially for a linearly polarized plane wave incidence, the subsequent change of its polarization is investigated and discussed.