The distribution of genes on eukaryotic chromosomes is nonrandom, but the reasons behind this are not well understood. The commonly observed clustering of essential genes is a case in point. Here we model and test a new hypothesis. Essential proteins are unusual in that random fluctuations in abundance (noise) can be highly deleterious. We hypothesize that persistently open chromatin domains are sinks for essential genes, as they enable reduced noise by avoidance of transcriptional bursting associated with chromatin remodeling. Simulation of the model captures clustering and correctly predicts that (i) essential gene clusters are associated with low nucleosome occupancy (ii) noise-sensitive nonessential genes cluster with essential genes (iii) nonessential genes of similar knockout fitness are physically linked (iv) genes in domains rich in essential genes have low noise (v) essential genes are rare subtelomerically and (vi) essential gene clusters are preferentially conserved. We conclude that different noise characteristics of different genomic domains favors nonrandom gene positioning. This has implications for gene therapy and understanding transgenic phenotypes.