The properties of the spin state manifold of the tetranuclear cluster Ni[(OH)(2)Cr(bispictn)]3}I-5.5H(2)O (bispictn = N,N'-bis(2-pyridylmethyl)-1,3-propanediamine) are investigated by combining magnetic susceptibility and magnetization measurements with an inelastic neutron scattering (INS) study on an undeuterated sample of Ni[(OH)(2)Cr(bispictn)](3)}I-5.5H(2)O. The temperature dependence of the magnetic susceptibility indicates an S = 1/2 ground state, which requires antiferromagnetic interactions both between Cr3+ and Ni2+ ions and among the Cr3+ ions. INS reveals potential single-ion anisotropies to be negligibly small and enables an accurate determination of the exchange parameters. The best fit to the experimental energy level diagram is obtained by an isotropic spin Hamiltonian H = J(CrNi)(S-1.S-4 + S-2.S-4 + S-3.S-4) + J(CrCr)(S-1.S-2 + S-1.S-3 + S-2.S-3) with J(CrNi) = 1.47 cm(-1) and J(CrCr) = 1.25 cm(-1). With this model, the experimental intensities of the observed INS transitions as well as the temperature dependence of the magnetic data are reproduced. The resulting overall antiferromagnetic exchange is rationalized in terms of orbital exchange pathways and compared to the situation in oxalato-bridged clusters.