  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 $SU(2)\times SU(2)\times U(1)$
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 $SU(2)\times SU(2)$ 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.
