We have studied assembly of chromatin on single DNAs using Xenopus egg extracts and magnetic tweezers. In the absence of ATP, interphase extracts assembled nucleosomes against DNA tensions of up to 3.5 piconewtons (pN). We observed force-induced disassembly and opening-closing fluctuations indicating our experiments were in mechano-chemical equilibrium. We found that the ATP-depleted reaction can do mechanical work of 27 kcal/mol per nucleosome, providing a measurement of the free energy difference between core histone octamers on and off DNA. Addition of ATP leads to highly dynamic behavior; time courses show processive runs of assembly and disassembly of not observed in the -ATP case, with forces of 2 pN leading to nearly complete fiber disassembly. Our study shows that ATP hydrolysis plays a major role in nucleosome rearrangement and removal, and suggests that chromatin in vivo may be subject to continual assembly and disassembly.