Polymer chain dynamics of a nanostructured block copolymer electrolyte, polystyrene-block-poly(ethylene oxide) (SEO) mixed with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt, are investigated by neutron spin echo (NSE) spectroscopy on the 0.1-100 ns time scale and analyzed using the Rouse model at short times (t ≤ 10 ns) and the reptation tube model at long times (t ≥ 50 ns). In the Rouse regime, the monomeric friction coefficient increases with increasing salt concentration, as seen previously in homopolymer electrolytes. In the reptation regime, the tube diameters, which represent entanglement constraints, decrease with increasing salt concentration. The normalized longest molecular relaxation time, calculated from the NSE results, increases with increasing salt concentration. We argue that quantifying chain motion in the presence of ions is essential for predicting the behavior of polymer-electrolyte-based batteries operating at large currents.