The process of Sum Frequency Generation (SFG) in chiral Carbon Nanotubes (CNTs), with the exciting laser beams propagating along the CNT symmetry axis, is here investigated. First the general form of the first hyperpolarizability third rank tensor β for chiral CNTs is determined with group projector technique method applied to the Ln_p22 line group describing their symmetry. For this purpose, the group natural factorization has been adopted and the associated irreducible representations, parameterized in terms of helical quantum numbers, then used to construct the group projector operator in the relevant vector space. The method demonstrates that second harmonic generation is symmetry forbidden in the collinear geometry while, conversely, SFG is symmetry allowed. Subsequently, the SFG far-field radiation pattern has been modelled with a calculation scheme derived from antenna's theory and already used for simulation of Rayleigh scattering from a CNT. The method has been overhauled for describing the here considered nonlinear optical interaction. The study of the role played by two induced counter-propagating current density retarded waves in shaping the radiation pattern is addressed and simulations are reported in the limit regimes of strong and weak attenuation.