LaCoO3 thin films grown under epitaxial tensile strain exhibit a robust ferromagnetic insulating state that is absent in the bulk. Despite many studies, both experimental and computational, the microscopic origin of this phenomenon is not well understood. In this work, density functional theory calculations are used to systematically investigate the magnetic ground state of stoichiometric LaCoO3 under epitaxial strain equivalent to that imposed by a SrTiO3 substrate. The results identify a ferromagnetic insulating ground state characterized by a unique ordered array of high-spin (HS) and low-spin (LS) Co3+ ions. The spin state ordering is best described as 2 × 2 columns that consist of alternating HS and LS Co3+ ions, separated by planes of LS Co3+ ions. This leads to HS–LS–LS repeating sequence of Co3+ ions in both pseudocubic [100] and [010] directions. Analysis of the electronic structure confirms the presence of an insulating gap. Evaluation of the superexchange interactions reveal ferromagnetic interactions between HS Co3+ ions via 90° paths, and antiferromagnetic interactions via 180° paths, both of which are facilitated by empty σ* (eg) orbitals on the diamagnetic LS Co3+ ions. The strength and number of 90° ferromagnetic interactions are sufficient to overcome the competing 180° antiferromagnetic interactions stabilizing a ferromagnetic insulating state.