The gain and loss of functional transcription-factor binding sites has been proposed as a major source of evolutionary change in cis-regulatory DNA and gene expression. We have developed an evolutionary model to study binding site turnover that uses multiple sequence alignments to assess the evolutionary constraint on individual binding sites, and to map gain and loss events along a phylogenetic tree. We apply this model to study the evolutionary dynamics of binding sites of the Drosophila melanogaster transcription factor Zeste, using genome-wide in vivo (ChIP-chip) binding data to identify functional Zeste binding sites, and the genome sequences of D. melanogaster, D. simulans, D. erecta and D. yakuba to study their evolution. We estimate that more than 5 percent of functional Zeste binding sites in D. melanogaster were gained along the D. melanogaster lineage or lost along one of the other lineages. We find that Zeste bound regions have a reduced rate of binding site loss and an increased rate of binding site gain relative to flanking sequences. Finally, we show that binding site gains and losses are asymmetrically distributed with respect to D. melanogaster, consistent with lineage-specific acquisition and loss of Zeste-responsive regulatory elements.