Combining equilibrium and non-equilibrium molecular dynamics simulations with accurate carbon potentials, we determine the thermal conductivity \(\lambda\) of carbon nanotubes and its dependence on temperature. Our results suggest an unusually high value \({\lambda}{\approx}6,600\)~W/m\(\cdot\)K for an isolated (10,10) nanotube at room temperature, comparable to the thermal conductivity of a hypothetical isolated graphene monolayer or diamond. Our results suggest that these high values of \(\lambda\) are associated with the large phonon mean free paths in these systems; substantially lower values are predicted and observed for the basal plane of bulk graphite.