Thermal conductivity prediction remains an important subject in many scientific and engineering areas. Only recently has such prediction become possible on the basis of the first principles calculations, thus ensuring high quality results. Implementation of the methodology, however, is technically challenging and requires a lengthy development process. We thus introduce the Phonon Transport Simulator (PhonTS), a Fortran90, fully parallel code to perform such calculations. PhonTS possesses a large array of options and returns the thermal conductivity tensor together with related quantities, such as spectral thermal conductivity, phonon lifetimes, mean free paths and Grüneisen parameters. First principles calculations are implemented via convenient interfaces to widely-used third-party codes, while many classical potentials are included in PhonTS itself. The code is carefully validated against data published in the literature from various thermal conductivity computational techniques and against experimental data.