A highly asymmetric Ni(II) cluster [Ni(4)(OH)(OMe)(3)(Hphpz)(4)(MeOH)(3)](MeOH) (1) (H(2)phpz=3-methyl-5-(2-hydroxyphenyl)pyrazole) has been prepared and its structure determined by means of single-crystal X-ray diffraction by using synchrotron radiation. Variable-temperature bulk-magnetization measurements show that the complex exhibits intramolecular-ferromagnetic interactions leading to a spin ground state S=4 with close-lying excited states. Magnetization and high-frequency EPR measurements suggest the presence of sizable Ising-type magnetic anisotropy, with zero-field splitting parameters D=-0.263 cm(-1) and E=0.04 cm(-1) for the spin ground state, and an isotropic g value of 2.25. The presence of both axial and transverse anisotropy was confirmed through low-temperature specific heat determinations down to 300 mK, but no slow relaxation of the magnetization was observed by AC measurements down to 1.8 K. Interestingly, AC susceptibility measurements down to temperatures as low as 23 mK showed no indication of slow relaxation of the magnetization in 1. Thus, despite the presence of an anisotropy barrier (U approximately 4.21 cm(-1) for the purely axial limit), the magnetization relaxation remains extremely fast down to the lowest temperatures. The estimated quantum tunneling rate, Gamma>0.667 MHz, makes this complex a prime candidate for observation of coherent tunneling of the magnetization.