The authors present preliminary calculations of low-energy e⁺-N₂ elastic scattering using the Kohn variational method. They present results for the Sigma _g⁺ and Sigma _u⁺ scattering symmetries below the first electron excitation threshold at 8.59 eV incident position energy. The trial functions for the calculations include separable correlation functions of Sigma _g⁺, Sigma _u⁺, Pi _u and Pi _g electronic symmetries and the results agree with R-matrix calculations by Danby and Tennyson (1991). The calculations are carried out in a similar way to previous successful low-energy e⁺-H₂ scattering calculations. This paper shows that it is possible to apply the method used in the e⁺-H₂ scattering calculations to positron scattering by a target molecule, N₂, containing 14 electrons.