The quasiternary intermetallic compound URh1/3Ni2/3Al crystallizes in the hexagonal ZrNiAl-type of structure, like the parent compounds URhAl (ferromagnet, TC = 27 K) and UNiAl (antiferromagnet, TN = 19 K). A delicate balance between ferromagnetic and antiferromagnetic interactions leads to suppression of magnetic order. The low-temperature properties show all attributes of a non-Fermi-liquid system, i.e. divergence of the low-temperature specific heat divided by temperature, which behaves as -ln(T/T0), divergence of the magnetic susceptibility and absence of a T2 dependence in the electrical resistivity. URh1/3Ni2/3Al also exhibits an enhanced low-temperature specific heat of 225 mJ/molU K2. The compound can be classified as a NFL system in which the magnetic phase transition is at zero kelvin.