  We prove that the non-commutative Gross-Neveu model on the two-dimensional
Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing,
renormalizability can be achieved. However, in the massive case, this forces us
to introduce an additional counterterm of the form "psibar i gamma^{0}
gamma^{1} psi". The massless case is renormalizable without such an addition.
