The reaction of Co(NCS)2 with 3-bromopyridine leads to the formation of discrete complexes [Co(NCS)2(3-bromopyridine)4] (1), [Co(NCS)2(3-bromopyridine)2(H2O)2] (2), and [Co(NCS)2(3-bromopyridine)2(MeOH)2] (3) depending on the solvent. Thermogravimetric measurements on 2 and 3 show a transformation into [Co(NCS)2(3-bromopyridine)2]n (4), which upon further heating is converted to [{Co(NCS)2}2(3-bromopyridine)3]n (5), whereas 1 transforms directly into 5 upon heating. Compound 5 can also be obtained from solution, which is not possible for 4. In 4 and 5, the cobalt(II) cations are linked by pairs of μ-1,3-bridging thiocyanate anions into chains. In compound 4, all cobalt(II) cations are octahedrally coordinated (OC-6), as is usually observed in such compounds, whereas in 5, a previously unkown alternating 5- and 6-fold coordination is observed, leading to vacant octahedral (vOC-5) and octahedral (OC-6) environments, respectively. In contrast to 4, the chains in 5 are very efficiently packed and linked by π···π stacking of the pyridine rings and interchain Co···Br interactions, which is the basis for the formation of this unusual chain. The spin chains in 4 demonstrate ferromagnetic intrachain exchange and much weaker interchain interactions, as is usually observed for such linear chain compounds. In contrast, compound 5 shows almost single-ion-like magnetic susceptibility, but the magnetic ordering temperature deduced from specific heat measurements is twice as high as that in 4, which might originate from π···π stacking and Co···Br interactions between neighboring chains. More importantly, unlike all linear Co(NCS)2 chain compounds, a dominant antiferromagnetic exchange is observed for 5, which is explained by density functional theory calculations predicting an alternating ferro- and aniferromagnetic exchange within the chains. Theoretical calculations on the two different cobalt(II) ions present in 5 predict an easy-axis anisotropy that is much stronger for the octahedral cobalt(II) ion than for the one with the vacant octahedral coordination, with the magnetic axes of the two ions being canted by an angle of 84°. This almost orthogonal orientation of the easy axis of magnetization for the two cobalt(II) ions is the rationale for the observed non-Ising behavior of 5.