© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. We study a lattice field theory described by two flavors of massless staggered fermions interacting with U(1) gauge fields in the strong coupling limit. We show that the lattice model has a SU(2)×SU(2) ×U(1) chiral symmetry and can be used to model the two-flavor QCD chiral phase transition in the absence of the anomaly. It is also possible to add a coupling to this model which breaks the chiral symmetry to SU(2) ×SU(2) and thus mimics the effects of the anomaly in two-flavor QCD. We construct an efficient directed loop algorithm to study such a model. We show that the chiral phase transition in our model is first order in the absence of the anomaly, while it becomes second order with O(4) exponents when the anomaly is turned on.