Ionically conducting polymers (salts dissolved in a polymer matrix) are of great interest because they uniquely exhibit ionic conductivity in a soft but solid membrane. As such, they are critical to the development of devices such as all-solid-state lithium batteries. The established view of ionic conductivity in polymer electrolytes is that this occurs in amorphous materials above their glass transition temperature and that crystalline polymer electrolytes are insulators. In contrast, we show that three crystalline polymer electrolytes, poly(ethylene oxide)(6):LiXF6, X=P, As, Sib, not only conduct but do so better than the analogous amorphous phases! It is also shown that the conductivities of all three 6:1 complexes are similar, consistent with the dimension of the bottlenecks to conduction derived from their crystal structures. An increase in ionic conductivity with reduction of molecular weight of the crystalline polymer electrolyte (from 2000 to 1000) is reported and shown to relate to the increase in crystallite size on reducing molecular weight.