Based on a sample of 355 quasars with significant optical polarization, we found that quasar polarization vectors are not randomly oriented over the sky as naturally expected. The probability that the observed distribution of polarization angles is due to chance is lower than 0.1%. The polarization vectors of the light from quasars are aligned although the sources span huge regions of the sky (˜ 1 Gpc). Groups of quasars located along similar lines of sight but at different redshifts (typically z ≍ 0.5 and z ≍ 1.5) are characterized by different preferred directions of polarization. These characteristics make the observed alignment effect difficult to explain in terms of a local contamination by interstellar polarization in our Galaxy. Interpreted in terms of a cosmological-size effect, we show that the dichroism and birefringence predicted by a mixing between photons and very light pseudoscalar particles within a magnetic field can qualitatively reproduce the observations. We find that circular polarization measurements could help constrain this mechanism.