The Hippo signaling pathway regulates tissue growth and organ development in many animals, including humans. Pathway activity leads to inactivation of Yorkie (Yki), a transcriptional coactivator that drives expression of growth-promoting genes. In addition, Yki has been shown to recruit chromatin modifiers that enhance chromatin accessibility and thereby enhance Yki function. Here, we asked whether changes in chromatin accessibility that occur during DNA replication could also affect Yki function. We found that depletion of the chromatin assembly complex-1 (CAF-1) complex, a histone chaperone that is required for nucleosome assembly after DNA replication, in the wing imaginal epithelium leads to increased Hippo pathway target gene expression but does not affect expression of other genes. Yki shows greater association with target sites when CAF-1 is depleted and misregulation of target gene expression is Yki-dependent, suggesting that nucleosome assembly competes with Yki for pathway targets post-DNA replication. Consistent with this idea, increased target gene expression is DNA replication dependent and newly replicated chromatin at target sites shows marked nucleosome depletion when CAF-1 function is reduced. These observations suggest a connection between cell cycle progression and Hippo pathway target expression, providing insights into functions of the Hippo pathway in normal and abnormal tissue growth.