Histones play a crucial role in the organization of DNA in the nucleus, but their presence can prevent interactions with DNA binding proteins responsible for repair of DNA damage. Uracil is an abundant mutagenic lesion recognized by uracil DNA glycosylase (UDG) in the first step of base excision repair (BER). In nucleosome core particles (NCPs), we find substantial differences in UDG-directed cleavage at uracils rotationally positioned toward (U-In) or away from (U-Out) the histone core, or midway between these orientations (U-Mid). Whereas U-Out NCPs show a cleavage rate just below that of naked DNA, U-In and U-Mid NCPs have markedly slower rates of cleavage. Crosslinking of U-In DNA to histones in NCPs yields a greater reduction in cleavage rate but, surprisingly, yields a higher rate of cleavage in U-Out NCPs compared with uncrosslinked NCPs. Moreover, the next enzyme in BER, APE1, stimulates the activity of human UDG in U-Out NCPs, suggesting these enzymes interact on the surface of histones in orientations accessible to UDG. These data indicate that the activity of UDG likely requires "trapping" transiently exposed states arising from the rotational dynamics of DNA on histones.