Molecular chaperones, also known as heat-shock proteins, refold misfolded proteins and help other proteins reach their native conformation. Thanks to these abilities, some chaperones, such as the Hsp90 protein or the chaperonin GroEL, can buffer the deleterious phenotypic effects of mutations that alter protein structure and function. Hsp70 chaperones use a chaperoning mechanism different from Hsp90 and GroEL, and it is not known whether they can also buffer mutations. Here, we show that they can. To this end, we performed a mutation accumulation experiment in Escherichia coli, followed by whole-genome resequencing. Our sequence data shows that overexpression of the Hsp70 chaperone DnaK increases the tolerance of its clients for nonsynonymous nucleotide substitutions and nucleotide insertions and deletions. We also show that this elevated mutational buffering on short evolutionary time scales translates into differences in evolutionary rates on intermediate and long evolutionary time scales. To this end, we compared the evolutionary rates of DnaK clients and nonclients using the genomes of E. coli, Salmonella typhimurium, and 83 other gamma-proteobacterial species. We find that clients that interact strongly with DnaK evolve faster than weakly interacting clients. Our results imply that all three major chaperone classes can buffer mutations and affect protein evolution. They illustrate how an individual protein like a chaperone can have a disproportionate effect on proteome evolution.