Summary: Motivated by recent investigations of transport properties of strongly correlated 1D models and thermal conductivity measurements of quasi 1D magnetic systems, we present results for the integrable \(\text{spin-} \frac 12 XXZ\) chain. The thermal conductivity \(\kappa (\omega)\) of this model has \(\text{Re} \kappa(\omega) =\widetilde \kappa\delta (\omega)\), i.e. it is infinite for zero frequency \(\omega\). The weight \(\widetilde\kappa\) of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low- and high-temperature limits are studied analytically.