Chain exchange kinetics of diblock copolymer micelles with lower critical micellization temperature (LCMT) phase behavior were investigated using time-resolved small-angle neutron scattering (TR-SANS). Three nearly identical isotopically substituted pairs of poly(methyl methacrylate)-block-poly(n-butyl methacrylate) (PMMA-b-PnBMA) diblocks were used in mixtures of the room temperature ionic liquids 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. In this case, the h-PnBMA and d9-PnBMA blocks form the micellar cores. The results are consistent with previous measurements in other systems, in that the barrier to chain extraction scales linearly with the core block length. By varying the ratio of the two homologous solvents in the mixture, the value of χ between the core block and the solvent is varied systematically. The results show that the solvent selectivity has a remarkable effect on the chain exchange rate, as anticipated by a previous theory. However, in contrast to an assumption in previous studies, we find that the barrier to chain exchange is not simply proportional to χ. Accordingly, we propose a more elaborate function of χ for the energy barrier, which is rationalized by a calculation in the spirit of Flory-Huggins theory. This modification can account for the chain exchange behavior when χ is relatively modest, i.e., in the vicinity of the critical micelle temperature.