Traditional polymers are both electrically and thermally insulating. The development of electrically conductive polymers has led to novel applications such as flexible displays, solar cells, and wearable biosensors. As in the case of electrically conductive polymers, the development of polymers with high thermal conductivity would open up a range of applications in next-generation electronic, optoelectronic, and energy devices. Current research has so far been limited to engineering polymers either by strong intramolecular interactions, which enable efficient phonon transport along the polymer chains, or by strong intermolecular interactions, which enable efficient phonon transport between the polymer chains. However, it has not been possible until now to engineer both interactions simultaneously. We report the first realization of high thermal conductivity in the thin film of a conjugated polymer, poly(3-hexylthiophene), via bottom-up oxidative chemical vapor deposition (oCVD), taking advantage of both strong C=C covalent bonding along the extended polymer chain and strong π-π stacking noncovalent interactions between chains. We confirm the presence of both types of interactions by systematic structural characterization, achieving a near-room temperature thermal conductivity of 2.2 W/m·K, which is 10 times higher than that of conventional polymers. With the solvent-free oCVD technique, it is now possible to grow polymer films conformally on a variety of substrates as lightweight, flexible heat conductors that are also electrically insulating and resistant to corrosion.