A long-standing question in extragalactic astrophysics is the composition of the relativistic jets of plasma that stream from the nuclei of quasars and active galaxies-do they consist of a `normal' (electron-proton) plasma, or a `pair' (electron-positron) plasma? Distinguishing between these possibilities is crucial for understanding the physical processes occurring close to the putative supermassive black holes that are believed responsible for the jets. Here we report the detection of circularly polarized radio emission from the jets of the archtypal quasar 3C279. The circular polarization is produced by Faraday conversion, which requires the energy distribution of the radiating particles to extend to very low energies, indicating that electron-positron pairs are an important component of the jet plasma. Similar detections in three other radio sources suggest that, in general, extragalactic radio jets are composed mainly of an electron-positron plasma.