A double Tl-O layer superconductor with three CuO 2 sheets in the Tl-Sr-Ca-Cu-O system, (Tl 1 - x Hg x ) 2 Sr 2 Ca 2 Cu 3 O y (x=0.35), has been synthesized under high-pressure and high-temperature for the first time. Incorporation of Hg appears to stabilize a double-layer Tl/Sr system in a manner similar to the role that Pb plays in the Bi/Sr system. Structural analyses, based on X-ray and electron diffractions and high-resolution transmission electron microscopy, have revealed a body-centered tetragonal unit cell that has lattice parameters a=3.8 Å and c=34.7 Å and isostructural with the Tl/Ba-2223 phase with the Ba-sites occupied by Sr. As-prepared samples exhibited bulk superconductivity below 103 K. (Tl 1 - x Hg x ) 2 Sr 2 CaCu 2 O y (x=0.35), has also been synthesized under 3 GPa and showed superconducting transition at 60 K, which is 35 K higher than that reported for the ambient pressure samples.