Moonlighting proteins exhibit functions that are alternative to their main role in the cell. Heat-shock proteins, also known as molecular chaperones, are now recognized for their wide range of activities in and/or outside the cell, being prominent examples of moonlighting proteins. Chaperonins are highly conserved molecular chaperones that fold other proteins into their native conformation allowing them to carry out essential functions in the cell. Activities alternative to folding have been reported for the chaperonin (Cpn) 60 protein. Preservation of various alternative functions in one protein conflicts with the optimization of each of the functions. What evolutionary mechanisms have allowed the persistence of moonlighting proteins, and in particular the chaperonins, remains a mystery. In the present article, I argue that mechanisms that increase the resistance of phenotypes to genetic and environmental perturbations enable the persistence of a reservoir of genetic variants, each potentially codifying for a distinct function. Gene duplication is one such mechanism that has characterized the expansion and has been concomitant with the emergence of novel functions in these protein families. Indeed, Cpn60 performs a large list of folding-independent functions, including roles in the transmission of viruses from insects to plants and stimulation of the immune system, among others. In addition to the innovation promoted by gene duplication, I discuss that the Cpn60 protein comprises a hidden amino acid combinatorial code that may well be responsible for its ability to develop novel functions while maintaining an optimized folding ability. The present review points to a complex model of evolution of protein moonlighting.