Estimates of heritability inform evolutionary potential and the likely outcome of many management actions, but such estimates remain scarce for marine organisms. Here, we report high heritability of calcification rate among the eight most dominant Hawaiian coral species under reduced pH simulating future ocean conditions. Coral colonies were sampled from up to six locations across a natural mosaic in seawater chemistry throughout Hawai'i and fragmented into clonal replicates maintained under both ambient and high pCO2 conditions. Broad sense heritability of calcification rates was high among all eight species, ranging from a low of 0.32 in Porites evermanni to a high of 0.61 in Porites compressa. The overall results were inconsistent with short-term acclimatization to the local environment or adaptation to the mean or ideal conditions. Similarly, in 'local vs. foreign' and 'home vs. away' tests there was no clear signature of local adaptation. Instead, the data are most consistent with a protected polymorphism as the mechanism which maintains differential pH tolerance within the populations. Substantial individual variation, coupled with high heritability and large population sizes, imply considerable scope for natural selection and adaptive capacity, which has major implications for evolutionary potential and management of corals in response to climate change.