We have used the analytical ultracentrifuge to measure the ability of histone octamers to compact DNA as a function of DNA supercoiling. Plasmid DNA (3.25 kb) was prepared at various linking numbers (ΔLk), ranging from -35 to +8. Relaxed plasmid (ΔLk = 0) was the least compact. We reconstituted a fixed number of nucleosome cores (either 11 or 13) on these DNAs. The dependence of the frictional coefficient of ΔLk showed that the reconstitute with an initial number of negative supercoils equal to the number of nucleosome cores was the least compact, as expected if each nucleosome core formed requires the constraint of one negative supercoil, resulting in relaxed linker DNA. With DNAs containing an initial number of negative supercoils unequal to the number of nucleosome cores, reconstitutes contained either negative or positive unconstrained supercoils. Reconstitutes with the same number of unconstrained supercoils, whether positive or negative, have similar frictional coefficients and are, therefore, compacted to similar degrees. We conclude that nucleosome cores compact positively and negatively supercoiled DNA equally well. Thus, nucleosome cores formed on positively supercoiled DNA with a superhelical density as high as +0.07 are not significantly unfolded.