The β decay of ^{208}Hg into the one-proton hole, one neutron-particle _{81}^{208}Tl_{127} nucleus was investigated at CERN-ISOLDE. Shell-model calculations describe well the level scheme deduced, validating the proton-neutron interactions used, with implications for the whole of the N>126, Z<82 quadrant of neutron-rich nuclei. While both negative and positive parity states with spin 0 and 1 are expected within the Q_{β} window, only three negative parity states are populated directly in the β decay. The data provide a unique test of the competition between allowed Gamow-Teller and Fermi, and first-forbidden β decays, essential for the understanding of the nucleosynthesis of heavy nuclei in the rapid neutron capture process. Furthermore, the observation of the parity changing 0^{+}→0^{-}β decay where the daughter state is core excited is unique, and can provide information on mesonic corrections of effective operators.