Mineralization at the supergiant Cu-U-Au-Ag Olympic Dam deposit (South Australia), the 'uranium endmember' of the iron-oxide copper-gold (IOCG) spectrum of ore deposits, is hosted in a breccia complex developed entirely within granite of the 1.59 Ga Hiltaba Suite (Gawler Craton). Earlier studies suggested brecciation and mineralization occurred within a magmatically-driven hydrothermal system at 1.59 Ga, with a critical role for mafic-ultramafic intrusions. In contrast, recent radiometric dating of the breccia complex indicates a prolonged, multi-stage history of brecciation and mineralization from 1.59 to 0.5-0.4 Ga. Ca-Fe-Mg-Mn-carbonate gangue minerals are associated with ore minerals at virtually every stage of mineralization. In a companion study (Apukhtina et al., 2020), this mineralogically, texturally and compositionally diverse carbonate mineral suite was assigned to seven associations defined on the basis of host lithology and texture. Here we report Sm-Nd, Pb-Pb and Lu-Hf isotope ages for these carbonates, which are used to examine the chronology of carbonate deposition. Initial Sr-Nd isotopic compositions are used to place constraints on fluid sources. Sm-Nd and Pb-Pb isotope systematics of calcite veins in ~1.59 Ga IOCG ore indicate 1.59-1.55 Ga deposition ages. Likewise, locally abundant laminated siderites have Sm-Nd ages in this age interval. A world-first attempt to apply Lu-Hf dating to carbonate gangue in an ore deposit yields ages that are 70-100 Ma younger than corresponding Sm-Nd ages, presumably reflecting isotopic exchange of carbonate Lu-Hf isotope systems with host rocks. Sm-Nd ages for carbonates assigned to other carbonate associations (hosted in highly altered inferred 1.59 Ga basalt and picrite; diverse settings within granite-dominated breccia; locally abundant megaclasts of green and red bedded sandstone/mudstone sequences; ~0.82 Ga doleritic dykes) are more diverse and range from ~1.59 to 0.5 Ga. The structurally youngest carbonates (unbrecciated fluorite-barite veins; carbonate matrix in polymict conglomerate above the breccia complex) yield ~0.50 Ga Sm-Nd ages. Inferred carbonate ages are broadly consistent with radiometric dates for other hydrothermal minerals (e.g., hematite, uraninite, apatite, fluorite). They suggest that mineralization initiated at 1.59 Ga was reworked and possibly increased in size in response to large-scale tectonic, magmatic, sedimentary and hydrothermal events. Initial ⁸⁷Sr/⁸⁶Sr in the carbonates is higher and more variable (0.710-0.752, average ~0.721) than could be explained by ore and gangue mineral formation from magmatic-hydrothermal fluids during a single event at 1.59 Ga, a model favored in several earlier studies. By contrast, carbonate formation over a long period, as inferred from the Sm-Nd chronology presented here, would allow ingrowth of ⁸⁷Sr in the granitic host rocks to develop the heterogeneous initial ⁸⁷Sr/⁸⁶Sr recorded in the carbonates. Carbonate-bearing fluids appear to have sourced Nd (and most likely also Sr) locally, within the host granite and breccia, with contributions from mafic rocks. The emerging evidence for protracted, multi-stage mineralization implies that single-stage models for Olympic Dam need to be revisited and that all studies of sulfide and gangue minerals in this deposit require careful radiometric dating. We speculate that the polymetallic nature and unusually large metal reserves of the Olympic Dam mineralization are related to its multi-stage formation history.