Plant floral stem cells divide a limited number of times before they stop and terminally differentiate, but the mechanisms that control this timing remain unclear. The precise temporal induction of the Arabidopsis zinc finger repressor KNUCKLES (KNU) is essential for the coordinated growth and differentiation of floral stem cells. We identify an epigenetic mechanism in which the floral homeotic protein AGAMOUS (AG) induces KNU at similar to 2 days of delay. AG binding sites colocalize with a Polycomb response element in the KNU upstream region. AG binding to the KNU promoter causes the eviction of the Polycomb group proteins from the locus, leading to cell division-dependent induction. These analyses demonstrate that floral stem cells measure developmental timing by a division-dependent epigenetic timer triggered by Polycomb eviction.