Uranium copper aluminide, UCu6.68Al4.32, has been synthesized by arc-melting, followed by annealing at 600 degrees C. The phase belongs to the tetragonal BaCd11-type (space group I4(1)/amd, Pearson symbol tI48, Z = 4, a = 10.2471(4) and c = 6.5883(3) angstrom, V = 691.78(4) angstrom(3)). Electrical resistivity, specific heat and magnetic susceptibility data, measured from room temperature down to 3 K do not show any magnetic phase transition. The compound stays in its paramagnetic state, and at high temperatures can be adjusted according to the modified Curie-Weiss model (mu(eff) similar to 2.7 mu(B)/U-atom). The Sommerfeld value of the specific heat, gamma similar to 98 mJ/molK(2), is well above the values derived for simple metallic systems. In this context, with the overall shape of the temperature dependent electrical resistivity, spin fluctuations can be concluded, dominating the ground state behaviour in UCu6.68Al4.32.