A new NMR experiment is presented for the measurement of mus-ms time scale dynamics of Asn and Gin side chains in proteins. Exchange contributions to the N-15 line widths of side chain residues are determined via a relaxation dispersion experiment in which the effective nitrogen transverse relaxation rate is measured as a function of the number of refocusing pulses in constant-time, variable spacing CPMG intervals. The evolution of magnetization from scalar couplings and dipole-dipole cross-correlations, which has limited studies of exchange in multi-spin systems in the past, does not affect the extraction of accurate exchange parameters from relaxation profiles of NH2 groups obtained in the present experiment. The utility of the method is demonstrated with an application to a Leu --> Ala cavity mutant of T4 lysozyme, L99A. II is shown that many of the side chain amide groups of Asn and Gin residues in the C-terminal domain of the protein are affected by a chemical exchange process which may be important in facilitating the rapid binding of hydrophobic ligands to the cavity.