Using the human genome sequence, the just published chimpanzee genome sequence, and measured expression levels of genes in several different tissues, the Max Planck Institute for Evolutionary Anthropology has been studying the evolution of mRNA expression in these closely related species. The data indicates that most of the thousands of observed changes in gene expression have not been selected due to beneficial effects. Selection against deleterious effects shows a strong pattern. Curiously, it seems that tissues differ in the level that they are affected by mutations: thus liver is least constrained, and allows most changes, whereas brain allows least. We also see indications that more changes in gene expression occurred in brain during the evolution of humans than occurred during the evolution of chimpanzees since both of them diverged from their last common ancestor.