Methylation of histone 3 lysine 4 (H3K4) by yeast Set1-COMPASS requires prior monoubiquitination of histone H2B. To define whether other residues within the histones are also required for H3K4 methylation, we systematically generated a complete library of the alanine substitutions of all of the residues of the four core histones in Saccharomyces cerevisiae. From this study we discovered that 18 residues within the four histones are essential for viability on complete growth media. We also identified several cis-regulatory residues on the histone H3 N-terminal tail, including histone H3 lysine 14 (H3K14), which are required for normal levels of H3K4 trimethylation. Several previously uncharacterized trans-regulatory residues on histones H2A and H2B form a patch on nucleosomes and are required for methylation mediated by COMPASS. This library will be a valuable tool for defining the role of histone residues in processes requiring chromatin.