The new oxofluoride Cu7(TeO3)6F2 has been synthesized by hydrothermal synthesis. It crystallizes in the triclinic system, space group P1. The crystal structure constitutes a Cu-O framework with channels extending along [001] where the F(-) ions and the stereochemically active lone-pairs on Te(4+) are located. From magnetic susceptibility, specific heat, and Raman scattering measurements we find evidence that the magnetic degrees of freedom of the Cu-O-Cu segments in Cu7(TeO3)6F2 lead to a mixed dimensionality with single Cu S = (1)/2 moments weakly coupled to spin-chain fragments. Due to the weaker coupling of the single moments, strong fluctuations exist at elevated temperatures, and long-range magnetic ordering evolves at comparably low temperatures (TN = 15 K).