The regulation of chromatin mobility in response to DNA damage is important for homologous recombination in yeast. Anchorage reduces rates of recombination, whereas increased chromatin mobility correlates with more efficient homology search. Here we tracked the mobility and localization of spontaneous S-phase lesions bound by Rad52, and find that these foci have reduced movement, unlike enzymatically induced double-strand breaks. Moreover, spontaneous repair foci are positioned in the nuclear core, abutting the nucleolus. We show that cohesin and nucleolar integrity constrain the mobility of these foci, consistent with the notion that spontaneous, S-phase damage is preferentially repaired from the sister chromatid.