The magnetic-field-induced birefringence in a ferrofluid composed of spherical cobalt nanoparticles has been studied both experimentally and theoretically. The considerable induced birefringence determined experimentally has been attributed to the formation of chains of nanoparticles. The birefringence has been measured as a function of the external magnetic field and the volume fraction (f) of nanoparticles. It is quadratic in f as opposed to the Faraday effect, which is linear in f. Experimental results agree well with the theoretical model based on a simple density functional approach. For dilute solutions the experimental results can be explained by assuming that only dimers of nanoparticles are formed while the concentration of longer chains is negligible.