The pervasive role of distant chromatin interactions in transcriptional regulation is increasingly becoming evident. There is a possibility that the greater diversity in chromatin interactions of a genomic locus could contribute to stochastic variation in its gene expression. However, this issue has not been addressed. Here, I present a few lines of evidence, which suggest that the variation in trans chromatin interactions might occur at the cost of expression noise. Genomic regions with nucleosome depletion, abundant and rapid transcription and with essential gene clusters exhibit relatively fewer trans chromatin interactions in the nucleus. Moreover, loci with greater number of interactions tend to show higher expression noise. Based on these observations, I hypothesize that the three dimensional organization of eukaryotic genomes might have evolved under a selective pressure to minimize the expression noise of essential gene clusters in the nucleus.