We have employed a novel multichannel transmission ellipsometer based on the rotating-compensator principle to characterize a MgF2 thin film helicoidal bianisotropic medium (HBM) deposited on a glass substrate. A HBM is a rotationally inhomogeneous anisotropic material obtained in thin film form by deposition at a glancing angle onto a rotating substrate to yield helical columns or helices with (i) an alignment perpendicular to the substrate surface, (ii) an in-plane scale of the order of nanometres, and (iii) a helix pitch of the order of the wavelength of visible light. The rotating-compensator multichannel ellipsometer provides a complete description of the optical response of this material to an incident linearly polarized plane wave. Evidence is introduced for circularly birefringent and dichroic behavior based on the observed rotation and ellipticity imparted to a linearly polarized monochromatic plane wave when it is transmitted at normal incidence through the ambient/HBM/substrate system. The spectra in both the optical rotation and ellipticity exhibit strong features in a narrow wavelength zone (430-450 nm) not unlike the Cotton effect in isotropic chiral media. The features in the experimental spectra are found to be in accord with theoretical predictions, using values for the pitch of the helices and their packing density estimated from scanning electron microscopy and gravimetry, respectively.