We construct a fermionic lattice model containing interacting spin-half fermions with an O(4) symmetry. In addition the model contains a Z2 chiral symmetry which prevents a fermion mass term. Our model is motivated by the ability to study its physics using the meron-cluster algorithm. By adding a strong repulsive Hubbard interaction U, we can transform it into the regular Heisenberg anti-ferromagnet. While we can study our model in any dimension, as a first project we study it in one spatial dimension. We discover that our model at U=0 can be described as a lattice-regularized 2-flavor Gross-Neveu model, where fermions become massive since the Z2 chiral symmetry of the model is spontaneously broken. We show numerically that the theory remains massive when U is small. At large values of U the model is equivalent to the isotropic spin-half anti-ferromagnetic chain, which is massless for topological reasons. This implies that our model has a quantum phase transition from a Z2 broken massive phase to a topologically massless phase as we increase U. We present results obtained from our quantum Monte Carlo method near this phase transition.