Lithium batteries rely crucially on fast charge and mass transport of Li+ in the electrolyte. For liquid and polymer electrolytes with added lithium salts, Li+ couples to the counter-anion to form ionic clusters that produce inefficient Li+ transport and lead to Li dendrite formation. Quantification of Li+ transport in glycerol-salt electrolytes via NMR experiments and MD simulations reveals a surprising Li+-hopping mechanism. The Li+ transference number, measured by ion-specific electrophoretic NMR, can reach 0.7, and Li+ diffusion does not correlate with nearby ion motions, even at high salt concentration. Glycerol's high density of hydroxyl groups increases ion dissociation and slows anion diffusion, while the close proximity of hydroxyls and anions lowers local energy barriers, facilitating Li+ hopping. This system represents a bridge between liquid and inorganic solid electrolytes, thus motivating new molecular designs for liquid and polymer electrolytes to enable the uncorrelated Li+-hopping transport needed for fast-charging and all-solid-state batteries.