In this paper, we introduce the Triplet Sombor Index (TSO), a new degree–based topological index defined over connected triples of vertices. We also establish several basic properties and bounds of the index in terms of graph parameters. In particular, we determine extremal trees with respect to TSO, and we prove that among all trees with \( n \) vertices, the star graph \( S_n \) achieves the maximum Triplet Sombor Index, while the path graph \( P_n \) attains the minimum value. Some structural properties and illustrative examples are also discussed.