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 rather than 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.