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Abstract Protein stability is a major constraint on protein evolution. Molecular chaperones, also known as heat-shock proteins, can relax this constraint and promote protein evolution by diminishing the deleterious effect of mutations on protein stability and folding. This effect, however, has only been stablished for a few chaperones. Here, we use a comprehensive chaperone-protein interaction network to study the effect of all yeast chaperones on the evolution of their protein substrates, that is, their clients. In particular, we analyze how yeast chaperones affect the evolutionary rates of their clients at two very different evolutionary time scales. We first study the effect of chaperone-mediated folding on protein evolution over the evolutionary divergence of Saccharomyces cerevisiae and S. paradoxus. We then test whether yeast chaperones have left a similar signature on the patterns of standing genetic variation found in modern wild and domesticated strains of S. cerevisiae. We find that genes encoding chaperone clients have diverged faster than genes encoding nonclient proteins when controlling for their number of protein-protein interactions. We also find that genes encoding client proteins have accumulated more intra-specific genetic diversity than those encoding nonclient proteins. In a number of multivariate analyses, controlling by other well-known factors that affect protein evolution, we find that chaperone dependence explains the largest fraction of the observed variance in the rate of evolution at both evolutionary time scales. Chaperones affecting rates of protein evolution mostly belong to two major chaperone families: Hsp70s and Hsp90s. Our analyses show that protein chaperones, by virtue of their ability to buffer destabilizing mutations and their role in modulating protein genotype-phenotype maps, have a considerable accelerating effect on protein evolution.