Abstract The scaling limit of the higher level Bethe Ansatz (HLBA) equations for a macroscopically half-filled Hubbard chain is considered. These equations practically decouple into three disjoint sets which are again of the BA type, and correspond to the secular equations of three different kinds of dressed particles (one massive and two massless). The finite size corrections and the fine structure of the spectrum show that the massless sector corresponds to a conformal field with central charge c = 1 and Gaussian anomalous dimensions. The zero temperature free energy is also calculated and is found to be in perfect agreement with the results of a perturbative calculation in the SU(2) chiral Gross-Neveu (CGN) model. Some further arguments are presented supporting the identification of the model obtained as the relativistic limit of the half-filled Hubbard chain with the SU(2) CGN model.