Although reef-building corals are rapidly declining worldwide, responses vary both within and among species. The inter-individual differences are partly heritable, raising the possibility of a predictive model of bleaching in the wild that incorporates genomic as well as environmental data. Towards that goal, we generated a chromosome-scale genome assembly for the coral Acropora millepora and obtained whole genome sequences for 237 phenotyped samples collected at 12 reefs distributed along the Great Barrier Reef. There was little population structure among the reefs overall, but scanning for localized genomic regions with greater evidence of structure, we detected signatures of long-term balancing selection in the heat-shock co-chaperone sacsin. We further used 213 of the samples to conduct a genome-wide association study of bleaching and incorporated the polygenic score derived from it into a predictive model. These results thus set the stage for the use of genomics-based approaches in coral conservation strategies.