The mechanism of chain exchange in block polymer micelles at equilibrium is investigated using time-resolved small-angle neutron scattering (TR-SANS). The binary micelles are formed from blends of two poly(styrene-b-ethylene-alt- propylene) (PS-PEP) copolymers with different PS core block lengths, only one of which is contrast-matched with the solvent, squalane, so that the monitored scattering intensity only reflects the other species. Micelles prepared with an excess of deuterated PS chains (of the visible species) and those with the equivalent protonated PS chains are blended ("postmixed") at room temperature, where the exchange of chains is suppressed. At several elevated temperatures these samples were monitored by TR-SANS, in which mixing of isotope-labeled visible species gives systematic reduction of scattering signals with time and provides a quantitative way to characterize the micelle exchange kinetics. Within experimental error, the results for each labeled chain (i.e., longer or shorter) in the binary micelles are identical to those recently reported for the same labeled chains in the corresponding single block copolymer component micelles, thus proving that chain exchange in these micelles involves independent chain motion. This reinforces the important conclusions that the single-chain exchange mechanism dominates in the studied micelle solutions and that micelle fusion or fission events are rare.