RELATIVE OF EARLY FLOWERING 6 (REF6, also known as JMJ12) counteracts Polycomb-mediated gene silencing by removing methyl groups from trimethylated histone H3 lysine 27 (H3K27me3) in hundreds of genes in Arabidopsis thaliana. Here we show that REF6 function and genome-wide targeting require its four Cys2His2 zinc fingers, which directly recognize a CTCTGYTY motif. Motifs bound by REF6 tend to cluster and reside in loci with active chromatin states. Furthermore, REF6 targets CUP-SHAPED COTYLEDON 1 (CUC1), which harbors CTCTGYTY motifs, to modulate H3K27me3 levels and activate CUC1 expression. Loss of REF6 causes CUC1 repression and defects in cotyledon separation. In contrast, REF6 does not bind CUC2, encoding a close homolog of CUC1, which lacks the CTCTGYTY motif. Collectively, these results identify a new targeting mechanism of an H3K27 demethylase to counteract Polycomb-mediated gene silencing that regulates plant development, including organ boundary formation.