We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the chiral phase transition in two-flavor massless QCD. Our model allows us to vary the QCD anomaly and thus study its effects on the transition. Our study confirms the widely accepted viewpoint 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 ~ 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.