The endocycle is a developmentally programmed variant cell cycle in which cells undergo repeated rounds of DNA replication with no intervening mitosis. In Drosophila, the endocycle is driven by the oscillations of Cyclin E/Cdk2 activity. How the periodicity of Cyclin E/Cdk2 activity is achieved during endocycles is poorly understood. Here, we demonstrate that the p21(cip1)/p27(kip1)/p57(kip2)-like cyclin-dependent kinase inhibitor (CKI), Dacapo (Dap), promotes replication licensing during Drosophila endocycles by reinforcing low Cdk activity during the endocycle Gap-phase. In dap mutants, cells in the endocycle have reduced levels of the licensing factor Double Parked/Cdt1 (Dup/Cdt1), as well as decreased levels of chromatin-bound minichromosome maintenance (MCM2-7) complex. Moreover, mutations in dup/cdt1 dominantly enhance the dap phenotype in several polyploid cell types. Consistent with a reduced ability to complete genomic replication, dap mutants accumulate increased levels of DNA damage during the endocycle S-phase. Finally, genetic interaction studies suggest that dap functions to promote replication licensing in a subset of Drosophila mitotic cycles.