  We use strongly coupled lattice QED with two flavors of massless staggered
fermions to model the physics of pions in two-flavor massless QCD. Our model
has the right chiral symmetries and can be studied efficiently with cluster
algorithms. In particular we can tune the strength of the QCD anomaly and thus
study its effects on the chiral phase transition. Our study confirms the widely
accepted view point that the chiral phase transition is first order in the
absence of the anomaly. Turning on the anomaly weakens the transition and turns
it second order at a critical anomaly strength. The anomaly strength at the
tricritical point is characterized using $r = (M_{\eta'}-M_{\pi})/\rho_{\eta'}$
where $M_{\eta'}, M_{\pi}$ are the screening masses of the anomalous and
regular pions and $\rho_{\eta'}$ is the mass-scale that governs the low energy
fluctuations of the anomalous symmetry. We estimate that $r \sim 7 $ in our
model. This suggests that a strong anomaly at the two-flavor QCD chiral phase
transition is necessary to wash out the first order transition.
