Evenly spaced nucleosomes directly correlate with condensed chromatin and gene silencing. The ATP-dependent chromatin assembly factor (ACF) forms such structures in vitro and is required for silencing in vivo. ACF generates and maintains nucleosome spacing by constantly moving a nucleosome towards the longer flanking DNA faster than the shorter flanking DNA. But how the enzyme rapidly moves back and forth between both sides of a nucleosome to accomplish bidirectional movement is unknown. We show that nucleosome movement depends cooperatively on two ACF molecules, suggesting that ACF functions as a dimer of ATPases. Further, the nucleotide state determines whether the dimer closely engages one vs. both sides of the nucleosome. Three-dimensional reconstruction by single particle electron microscopy of the ATPase-nucleosome complex in an activated ATP state reveals a dimer architecture in which the two ATPases face each other. Our results suggest a model in which the two ATPases work in a coordinated manner, taking turns to engage either side of a nucleosome, thereby allowing processive bidirectional movement. This novel dimeric motor mechanism differs from that of dimeric motors such as kinesin and dimeric helicases that processively translocate unidirectionally and reflects the unique challenges faced by motors that move nucleosomes.