Congenital heart disease (CHD) is the most frequent birth defect, affecting 0.8% of live births. Many cases occur sporadically and impair reproductive fitness, suggesting a role for de novo mutations. Here we compare the incidence of de novo mutations in 362 severe CHD cases and 264 controls by analysing exome sequencing of parent-offspring trios. CHD cases show a significant excess of protein-altering de novo mutations in genes expressed in the developing heart, with an odds ratio of 7.5 for damaging (premature termination, frameshift, splice site) mutations. Similar odds ratios are seen across the main classes of severe CHD. We find a marked excess of de novo mutations in genes involved in the production, removal or reading of histone 3 lysine 4 (H3K4) methylation, or ubiquitination of H2BK120, which is required for H3K4 methylation. There are also two de novo mutations in SMAD2, which regulates H3K27 methylation in the embryonic left-right organizer. The combination of both activating (H3K4 methylation) and inactivating (H3K27 methylation) chromatin marks characterizes 'poised' promoters and enhancers, which regulate expression of key developmental genes. These findings implicate de novo point mutations in several hundreds of genes that collectively contribute to approximately 10% of severe CHD.