We report an electron-beam based method for the nanoscale patterning of the poly(ethylene oxide)/LiClO4 polymer electrolyte. We use the patterned polymer electrolyte as a high capacitance gate dielectric in single nanowire transistors and obtain subthreshold swings comparable to conventional metal/oxide wrap-gated nanowire transistors. Patterning eliminates gate/contact overlap, which reduces parasitic effects and enables multiple, independently controllable gates. The method's simplicity broadens the scope for using polymer electrolyte gating in studies of nanowires and other nanoscale devices.