We report a ternary silver chalcogenide, Ag2Se0.5Te0.5, as a new topological material with improved quantum transport properties. Single-crystalline nanostructures of ternary silver chalcogenides Ag2SexTe1-x are synthesized with a tunable chemical composition via the chemical vapor transport method. Quantum transport studies reveal that Ag2Se0.5Te0.5 nanowires present topological surface states with higher electron mobility and longer mean free path compared to binary Ag-chalcogenides. First-principles calculations also indicate that Ag2Se0.5Te0.5 is a topological insulator, and the observed enhancement in transport properties could imply reduced bulk carrier contribution in the new ternary silver chalcogenide.