Populations of European ash trees (Fraxinus excelsior) are being devastated by the invasive alien fungus Hymenoscyphus fraxineus, which causes ash dieback. We sequenced whole genomic DNA from 1,250 ash trees in 31 DNA pools, each pool containing trees with the same ash dieback damage status in a screening trial and from the same seed-source zone. A genome-wide association study identified 3,149 single nucleotide polymorphisms (SNPs) associated with low versus high ash dieback damage. Sixty-one of the 192 most significant SNPs were in, or close to, genes with putative homologues already known to be involved in pathogen responses in other plant species. We also used the pooled sequence data to train a genomic prediction model, cross-validated using individual whole genome sequence data generated for 75 healthy and 75 damaged trees from a single seed source. The model's genomic estimated breeding values (GEBVs) allocated these 150 trees to their observed health statuses with 67% accuracy using 10,000 SNPs. Using the top 20% of GEBVs from just 200 SNPs, we could predict observed tree health with over 90% accuracy. We infer that ash dieback resistance in F. excelsior is a polygenic trait that should respond well to both natural selection and breeding, which could be accelerated using genomic prediction.