We have prepared a novel nickel(II) trinuclear compound [Ni₃(tmen)₃(μ₂-Cl)₃(μ₃-OMe)(μ₃-OH)](BPh₄)·0.5MeOH·0.5CH₂Cl₂ (1; tmen = N,N,N',N'-tetramethylethylenediamine) with a trigonal bipyramid molecular structure, where the basal plane consists of Ni₃(μ₂-Cl)₃ atoms. Two known compounds [Ni₃(tmen)₃X₄(OH)]X (X = Cl (2), Br (3)) were also investigated. The magnetic study clarified the ground high-spin (S = 3) state, and the intramolecular exchange coupling parameters were determined as 2J/k_B = 18.0±0.2, 27.2±0.2, and 19.6±0.2 K for 1, 2, and 3, respectively. The crystallographic analysis clarified the unique geometry of 1. The molecular axes are aligned almost parallel in the crystallographic b axis. Relatively short intermolecular ClCl distances (3.725(1) and 3.847(2) Å) are found among linearly arrayed complex ions. The single-crystal magnetic study gave a zero-field-splitting parameter D_S=3/k_B = −2.2±0.1 K. An intermolecular exchange coupling parameter was determined as 2j/k_B = −0.15±0.01 K from simulation. The pulsed-field magnetization study at 0.5 K for 1 showed a jump around 1.2 T, which is explained in terms of intermolecular interaction. The alternating current magnetic susceptibility measurements revealed the Arrhenius behavior with E_a = 10.1±0.8 K at zero bias field. Therefore, the magnetic properties of 1 can be understood as a quasi-chain made of weakly coupled potential single-molecule magnets.