The uniaxial chiral medium is a generalisation of the wellstudied isotropic chiral media. It is obtained when microscopic helices with parallel axes are positioned in a host dielectric in random locations. Solutions for the dispersion equation and for the eigenwaves for a uniaxial chiral medium were recently found. In the Letter, the polarisation properties of a transverse wave propagating through a uniaxial chiral slab are considered. The results give a simple possibility for constructing a polarisation transformer for changing the polarisation of a propagating plane wave.