We sequenced approximately 4.5 kb of mtDNA from 161 individuals representing 11 named taxa of giant Galápagos tortoises (Geochelone nigra) and about 4 kb of non-coding nuclear DNA from fewer individuals of these same 11 taxa. In comparing mtDNA and nucDNA divergences, only silent substitutions (introns, ITS, mtDNA control region, and synonymous substitutions in coding sequences) were considered. mtDNA divergence was about 30 times greater than that for nucDNA. This rate discrepancy for mtDNA and nucDNA is the greatest yet documented and is particularly surprising for large ectothermic animals that are thought to have relatively low rates of mtDNA evolution. This observation may be due to the somewhat unusual reproductive biology and biogeographic history of these organisms. The implication is that the ratio of effective population size of nucDNA/mtDNA is much greater than the usually assumed four. The nearly neutral theory of molecular evolution predicts this would lead to a greater difference between rates of evolution.