We characterized the relationship of H3K4me1 and H3K4me3 at distal and proximal regulatory elements by comparing ChIP-seq profiles for these histone modifications and for two functionally different transcription factors: STAT1 in the immortalized HeLa S3 cell line, with and without interferon-gamma (IFNG) stimulation; and FOXA2 in mouse adult liver tissue. In unstimulated and stimulated HeLa cells, respectively, we determined approximately 270,000 and approximately 301,000 H3K4me1-enriched regions, and approximately 54,500 and approximately 76,100 H3K4me3-enriched regions. In mouse adult liver, we determined approximately 227,000 and approximately 34,800 H3K4me1 and H3K4me3 regions. Seventy-five percent of the approximately 70,300 STAT1 binding sites in stimulated HeLa cells and 87% of the approximately 11,000 FOXA2 sites in mouse liver were distal to known gene TSS; in both cell types, approximately 83% of these distal sites were associated with at least one of the two histone modifications, and H3K4me1 was associated with over 96% of marked distal sites. After filtering against predicted transcription start sites, 50% of approximately 26,800 marked distal IFNG-stimulated STAT1 binding sites, but 95% of approximately 5800 marked distal FOXA2 sites, were associated with H3K4me1 only. Results for HeLa cells generated additional insights into transcriptional regulation involving STAT1. STAT1 binding was associated with 25% of all H3K4me1 regions in stimulated HeLa cells, suggesting that a single transcription factor can interact with an unexpectedly large fraction of regulatory regions. Strikingly, for a large majority of the locations of stimulated STAT1 binding, the dominant H3K4me1/me3 combinations were established before activation, suggesting mechanisms independent of IFNG stimulation and high-affinity STAT1 binding.