Solid polymer electrolytes (SPEs) have the potential to increase both the energy density and stability of lithium-based batteries, but low Li+ conductivity remains a barrier to technological viability. SPEs are designed to maximize Li+ diffusivity relative to the anion while maintaining sufficient salt solubility. It is thus remarkable that poly(ethylene oxide) (PEO), the most widely used SPE, exhibits Li+ diffusivity that is an order of magnitude smaller than that of typical counterions at moderate salt concentrations. We show that Lewis-basic polymers like PEO favor slow cation and rapid anion diffusion, while this relationship can be reversed in Lewis-acidic polymers. Using molecular dynamics, polyboranes are identified that achieve up to 10-fold increases in Li+ diffusivities and significant decreases in anion diffusivities, relative to PEO in the dilute-ion regime. These results illustrate a general principle for increasing Li+ diffusivity and transference number with chemistries that exhibit weaker cation and stronger anion coordination.