Motivated by anecdotal as well as econometric evidence from Italy, we ask whether private schools can provide lower quality than public schools. Using a stylized model of the education market with sequential entry of a public and a private school, we show that, depending on the underlying parameters of the model, a market structure with the private school offering at a positive price lower quality than the public school can be an equilibrium. The calibrated parameters for Italy suggest the existence of such an equilibrium in the Italian market for education.