The branchial epithelium is one of the main tissues in which histone H3K4 trimethylation (H3K4me3) occurs in the budding tunicate, Polyandrocarpa misakiensis. It contains proliferating and undifferentiated cell aggregates at the bottom of each pharyngeal cleft, providing the nest for the adult stem cell niche. We examined the sustainable mechanism enabling epigenetic histone methylation in adult stem cells. Histone H3K4 demethylase (PmisKdm5) was not co-expressed in vivo with the transcription factor, signal transduction and activator of transcription (PmisStat) in the same cells. PmisStat mRNA, when electroporated into zooids, suppressed the gene expression of PmisKdm5 and facilitated the trimethylation of H3K4. A STAT5 inhibitor blocked the nuclear localization of PmisStat. It stimulated PmisKdm5 gene expression irrespective of PmisStat mRNA. The KDM5 inhibitor, CPI-455, stimulated H3K4me3 similarly to PmisStat mRNA. PmisStat mRNA and CPI-455 both induced the gene expression of PmisAp2 and PmisSp8, which were recently identified as budding/regeneration-related genes. When zooid tissues were treated with both CPI-455 and the STAT5 inhibitor, CPI-455 overwhelmed the effects of the STAT inhibitor on PmisAp2 and PmisSp8. PmisStat is involved in epigenetic histone methylation at H3K4 through the inhibition of PmisKdm5. H3K4me3 affects downstream gene expression more directly and strongly than PmisStat.