Background/Context: Existing evaluations of the Knowledge is Power Program (KIPP) and the Harlem Children's Zone (HCZ) charter school programs suggest that these programs may potentially be very effective in closing the academic achievement gap. Purpose/Objective: The purpose of the current study is to investigate the possibility of an internal contradiction in the assumptions underlying the KIPP and HCZ models that would prevent the models from being scaled up with the same positive results. Research Design: The method involves: (1) review of the results of the key impact studies; (2) review of empirical evidence of high teacher attrition; (3) review of statements by the founders of the HCZ and KIPP models articulating the core assumption; (4) a narrative explanation of the internal contradiction in these models; and (5) a formal analysis demonstrating the consequences of this contradiction. Findings/Results: The analysis suggests that gains from the KIPP and HCZ models would fall to zero once these programs are implemented in every school across the nation. The analysis suggests why existing impact results are likely due to artifacts stemming from high teacher attrition and hoarding of a disproportionate share of the nation's limited pool of highly dedicated teachers, rather than gains that could be sustained when the programs are scaled up and implemented nationwide. Conclusions/Recommendations: The article recommends that national implementation of the KIPP and HCZ models should be delayed until research has been performed that would substantiate the assumption that there is a sufficient supply of highly dedicated teachers to fill the large number of vacant teaching positions that arise as a consequence of these models.