High thermal conductivity is critical for many applications of polymers (for example, packaging of light-emitting diodes), in which heat must be dissipated efficiently to maintain the functionality and reliability of a system. Whereas uniaxially extended chain morphology has been shown to significantly enhance thermal conductivity in individual polymer chains and fibers, bulk polymers with coiled and entangled chains have low thermal conductivities (0.1 to 0.4 W m(-1) K-1). We demonstrate that systematic ionization of a weak anionic polyelectrolyte, polyacrylic acid (PAA), resulting in extended and stiffened polymer chains with superior packing, can significantly enhance its thermal conductivity. Cross-plane thermal conductivity in spin-cast amorphous films steadily grows with PAA degree of ionization, reaching up to similar to 1.2 W m(-1) K-1, which is on par with that of glass and about six times higher than that of most amorphous polymers, suggesting a new unexplored molecular engineering strategy to achieve high thermal conductivities in amorphous bulk polymers.