The uniaxial bianisotropic medium is a generalisation of the bi-isotropic and chiral media which recently have been the subject to intensive research. Such a medium results, for example, when microscopic helices with parallel axes are positioned in a host dielectric in random locations. Plane wave propagation in such a medium is studied and a simple solution for the dispersion equation is found. Numerical examples for the wave number surfaces of the medium are given.