We investigate the synthesis of a thallium scandate, TlScO3, under high-pressure (6-7.7 GPa) and high-temperature (1373-1773 K) conditions. At 6 GPa, a LiNbO3-type phase appears in a narrow temperature range and in mixtures with other phases. At 7.7 GPa and 1673 K, a new LiNbO3-type oxide is found with a composition of (Tl1-xScx)ScO3 and x approximate to 0.26 as determined by structural analysis from X-ray powder diffraction data. It crystallizes in space group R3c (No. 161) with lattice parameters of a = 5.50283(7) angstrom and c = 14.4606(2) angstrom. It is stable at least up to 800 K at ambient pressure. The point-charge model gives an electric polarization of 60 mu C/cm(2). First-principles calculations show that centrosymmetric ilmenite-type and polar LiNbO3-type structures of stoichiometric TlScO3 have almost the same lowest energy, and the next stable structure is a GdFeO3-type perovskite structure.