Copper-based chalcogenides are cost-effective and environmentally friendly thermoelectric (TE) materials for waste heat recovery. Despite demonstrating excellent thermoelectric performance, binary Cu2X (X = S, Se, and Te) chalcogenides undergo superionic phase transitions above room temperature, leading to microstructural evolution and unstable properties. In this work, a new gamma-phase of Cu6Te3-xS1+x (0 < x <= 1) is discovered, a narrow-bandgap semiconductor with outstanding thermoelectric performance and high stability. By substituting Te with S in metallic Cu6Te3S, the crystal symmetry is modified and structural phase transitions are eliminated. The gamma-phase exhibits a significantly higher Seebeck coefficient of up to 200 <mu>VK-1 compared to 8.8 mu VK-1 for Cu6Te3S at room temperature due to optimized carrier concentration and increased effective mass. Cu6Te3-xS1+x materials also demonstrate ultralow thermal conductivity (approximate to 0.25 Wm(-1)K(-1)), which, in concert with improved power factors, enables a high zT of approximate to 1.1 at a relatively low temperature of 500 K. Unlike most Cu-based chalcogenides, the gamma-phase exhibits excellent transport property stability across multiple thermal cycles, making it a cost-effective and eco-friendly alternative to Bi2Te3-based materials. The developed Cu6Te3-xS1+x is a promising candidate for thermoelectric converters in waste heat recovery, and its potential can be further extended to cooling applications through carrier concentration tuning.