We study a rotation-invariant Majorana fermion model in one dimension using diagrammatic perturbation theory and numerical diagonalization of small systems. The model is inspired by a Majorana representation of the antiferromagnetic spin- chain, and it is similar in form to the t - J model of electrons, except that the Majorana fermions carry spin 1 and charge. We discuss the implications of our results for the low-energy excitations of the spin- chain. We also discuss a generalization of our model from three species of Majorana fermions to N species; the SO(4) symmetric model is particularly interesting.