The electronic magnetization of Eu3+ions at low temperatures is associated with Van Vleck temperature‐independent paramagnetism; the ground state hasJ=0. We have calculated the Faraday rotation for this ion. A contribution from the Van Vleck paramagnetism is partially cancelled by the usual diamagnetic term. The resulting rotation should be observable in Eu3+in the microwave and infrared regions. In the appropriate limits we find for the rotation per unit length&Dgr;&thgr;/&Dgr;x=(48&mgr;B2N/ℏ&ngr;)(ℏ&ohgr;/&Dgr;)4(&mgr;BH0/&Dgr;)[1−(ℏ&ohgr;/&Dgr;)2]−2,whereNis the concentration,vis the velocity of light in the medium, and &Dgr; is the splitting betweenJ=1 andJ=0. We give the appropriate modification of this formula in a crystal field. We calculate the gyromagnetic ratiog′; at low temperatures the calculations of Frank have to be corrected to take into account nuclear effects.