We construct a fully back-reacted holographic dual of a four-dimensional field theory which exhibits chiral symmetry breaking. Two possible models are considered by studying the effects of a five-dimensional field, dual to the $q\bar{q}$ operator. One model has smooth geometry at all radii and the other dynamically generates a cutoff at finite radius. Both of these models satisfy Einstein's field equations. The second model has only three free parameters, as in QCD, and we show that this gives phenomenologically consistent results. We also discuss the possibility that in order to obtain linear confinement from a back-reacted model it may be necessary to consider the condensate of a dimension two operator. ; Comment: 13 pages, 4 figures, Replaced with minor corrections