In this paper we examine the role of chirality or handedness on em (electromagnetic) wave propagation in a discrete random dielectric composite. Although chirality is manifested naturally by certain molecules and polymers at optical wavelengths, it must be introduced artificially at microwave frequencies. A discrete random medium is considered in which the inclusion phase is described by new constitutive equations, D = εE + βε∇×E and B = μ H + β μ ∇ × H. The new material constant β (meters), called the chirality parameter, arises due to the introduction of handedness in the material of which the inclusions are made. The influence of this parameter on the effective phase velocity and the attenuation of em waves is studied using a multiple scattering formalism that has previously been used successfully to describe dielectric composites that were nonchiral. The role of chirality in altering the propagation characteristics is readily apparent by comparing results for chiral and nonchiral media that are otherwise identical. Numerical results are presented for spherical inclusions made of a chiral material, for various concentrations and frequencies.