We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle θ13 while maintaining the tri-bimaximal predictions for the atmospheric angle θ23=45° and solar angle θ12=35°. We show how such tri-bimaximal-reactor mixing can arise at leading order from the (type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as A4, spontaneously broken by flavons with a particular vacuum alignment.