Trimethylation of histone H3 at lysine 4 (H3K4me3) is a chromatin modification known to mark the transcription start sites of active genes. Here, we show that H3K4me3 domains that spread more broadly over genes in a given cell type preferentially mark genes that are essential for the identity and function of that cell type. Using the broadest H3K4me3 domains as a discovery tool in neural progenitor cells, we identify novel regulators of these cells. Machine learning models reveal that the broadest H3K4me3 domains represent a distinct entity, characterized by increased marks of elongation. The broadest H3K4me3 domains also have more paused polymerase at their promoters, suggesting a unique transcriptional output. Indeed, genes marked by the broadest H3K4me3 domains exhibit enhanced transcriptional consistency and [corrected] increased transcriptional levels, and perturbation of H3K4me3 breadth leads to changes in transcriptional consistency. Thus, H3K4me3 breadth contains information that could ensure transcriptional precision at key cell identity/function genes.