Until recently, the neutrino mixing pattern was well-approximated by tribimaximal mixing (TBM). The results from the Daya Bay and Reno collaborations have called this paradigm into question and indicate that the reactor angle theta13 is non-zero with about 5sigma significance. Explaining the largeness of theta13 is now one of the major challenges in neutrino model building. Motivated by the fact that tribimaximal mixing is still a good prediction for the solar and atmospheric mixing angles, we present a supersymmetric model with a T7 family symmetry (w/o any abelian factors) that gives TBM at leading order. The particle content is that of the Standard Model plus two flavon fields, and the effective Lagrangian contains all terms of mass dimension <=6. We realize a large theta13 by considering the next-to-leading order (NLO) corrections to the superpotential. In general, the NLO corrections will not only increase theta13, but also change the values of theta12 and theta23. By realizing our effective Lagrangian as the low-energy limit of a renormalizable, more fundamental theory, we pick only those contributions that increase theta13 and do not appreciably change the other two mixing angles. Our model is minimal in the sense that T7 has only 21 elements and is thus smaller than any A4xZN symmetry group for which TBM has been realized so far.