The crystal structure of the first thallium-bearing gold telluride, honeaite Au3TlTe2, is reported and its topological novelty discussed. Honeaite is orthorhombic, space group Pbcm and unit-cell parameters a = 8.9671(4), b = 8.8758(4), c = 7.8419(5) Å, V = 624.14(6) Å3 (Z = 4). Its structure has been refined to R1 = 0.033, wR2 = 0.053, Goof = 1.087. The structure is based upon a corrugated double-sheet comprising two sub-sheets, each composed of six-membered rings of corner-linked TeAu3 pyramids in which the Te lone pair is stereoactive. Rows of thallium atoms lie in the grooves between sheets and provide the only inter-sheet connectivity via Tl-Au bonds. There is extensive Au-Au bonding linking the two sub-sheets of the double-sheet. The structure is distinct from those of the 1:2 (Au,Ag)-tellurides: calaverite AuTe2, sylvanite AuAgTe4 and krennerite Au3AgTe8, which are based upon sheet structures with no connecting inter-sheet atoms. It also differs fundamentally from the structures of synthetic phases Ag3TlTe2 and Ag18Tl4Te11, both of which have an analogous stoichiometry. In contrast to the pyramidal TeAu3 group of honeaite and krennerite, Ag does not form the corresponding TeAg3 group in its tellurides.