The concomitant folding of a protein with its synthesis on the ribosome is influenced by a number of different timescales including the translation rate. Here we present a kinetic formalism to describe cotranslational folding and predict the effects of variable translation rates on this process. Our approach, which utilizes equilibrium data from arrested ribosome nascent chain complexes, provides domain folding probabilities in quantitative agreement with molecular simulations of folding at different translation rates. We show that the effects of single codon mutations in messenger RNA that alter the translation rate can lead to a dramatic increase in the extent of folding under specific conditions. The kinetic formalism that we discuss can describe the cotranslational folding process occurring on a single ribosome molecule as well as for a collection of stochastically translating ribosomes.