A Carr-Purcell-Meiboom-Gill relaxation dispersion experiment is presented for quantifying millisecond time-scale chemical exchange at side-chain H-1 positions in proteins. Such experiments are not possible in a fully protonated molecule because of magnetization evolution from homonuclear scalar couplings that interferes with the extraction of accurate transverse relaxation rates. It is shown, however, that by using a labeling strategy whereby proteins are produced using {C-13,H-1}-glucose and D2O a significant number of 'isolated' side-chain H-1 spins are generated, eliminating such effects. It thus becomes possible to record H-1 dispersion profiles at the beta positions of Asx, Cys, Ser, His, Phe, Tyr, and Trp as well as the gamma positions of Glx, in addition to the methyl side-chain moieties. This brings the total of amino acid side-chain positions that can be simultaneously probed using a single H-1 dispersion experiment to 16. The utility of the approach is demonstrated with an application to the four-helix bundle colicin E7 immunity protein, Im7, which folds via a partially structured low populated intermediate that interconverts with the folded, ground state on the millisecond time-scale. The extracted H-1 chemical shift differences at side-chain positions provide valuable restraints in structural studies of invisible, excited states, complementing backbone chemical shifts that are available from existing relaxation dispersion experiments.