A new hydroxyl sulfate-fluoride compound, Lu2Cu(SO4)(2)(OH)(3)F center dot H2O, was obtained using a hydrothermal method. This compound is found to crystallize in a monoclinic space group of P2(1)/c, exhibiting a uniform chain structure along the b axis, in which the chains are composed of elongated CuO4+2 octahedra and further separated by SO4 tetrahedra and Lu3+ ions. The shortest Cu-Cu distance inside the chains is similar to 3.394(1) angstrom, while that between neighboring chains is similar to 7.878(1) angstrom. Magnetic and heat capacity measurements indicate that this compound does not possess long-range magnetic order until 2 K. The fitting of spin-chain models suggests a strong intrachain interaction J and a weak interchain interaction J' with a small value of vertical bar J'/J vertical bar < 3.20(2) x 10(-3), indicating that Lu2Cu(SO4)(2)(OH)(3)F center dot H2O may be a nearly ideal one-dimensional spin-1/2-chain system.