We used molecular dynamics simulations to calculate the thermal conductivity of polyethylene chains, by employing the widely used Green-Kubo formula. The simulations use the AIREBO potential and employ periodic boundary conditions to mimic the dynamics of an infinite chain. In this limiting case, we observed that when the simulation domain is large enough the thermal conductivity diverges. The results suggest that single polymer chains intrinsically have high thermal conductivity. Although polymers are generally known to have low thermal conductivity, our observation of divergent thermal conductivity in a single chain suggests that high thermal conductivity polymer materials can be engineered, which would be of interest to a wide range of applications.